Full List of Publications


WARNING: The electronic files included here are the
preprint versions and NOT the final published ones
2017
J144. Mielke, R. Patterson, M. Peletier, M. Renger. Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. SIAM J. Appl. Math., 77 (4): 1562-1585, 2017.
J143. M. Heida, A. Mielke. Averaging of time-periodic dissipation potentials in rate-independent processes, DCDS-S Discrete Contin. Dyn. Syst. Ser. S, 10 (6): 1303-1327, 2017.
M13. H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci. "PDE 2015: Theory and Applications of Partial Differential Equations", proceedings of PDE 2015, DCDS-S Discrete Contin. Dyn. Syst. Ser. S, 10 (4): pages i-iv + 933, 2017.
J142. M. Mittnenzweig, A. Mielke. An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. J. Stat. Physics 167 (2): 205-233, 2017.
J141. M. Liero, A. Mielke, M. Peletier, D.R.M. Renger. On microscopic origins of generalized gradient structures. DCDS-S Discrete Contin. Dyn. Syst. 10 (1): 1-35, 2017 (Proceedings of STAMM 2014 in Poitiers).
2016
J140. A. Mielke and T. Roubíček. Rate-independent elastoplasticity at finitesrains and its numerical approximation. Math. Models Meth. Appl. Sciences 26 (12): 2203-2236, 2016.
J139. M. Liero, A. Mielke, G. Savaré. Optimal transport in competition with reaction: The Hellinger-Kantorovich distance and geodesic curves. SIAM J. Math Analysis, 18: 2869-2911, 2016.
J138. A. Mielke, R. Rossi, G. Savaré. Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. J. Eur. Math. Soc. (JEMS), 18: 2107-2165, 2016.
J137. A. Mielke, M. Peletier, D.R.M. Renger. A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility. J. Non-Equilib. Thermodyn., 41 (2): 141-149, 2016.
J136. S. Heinz, A. Mielke. Existence, numerical convergence, and evolutionary relaxation for a rate-independent phase-transformation model. Phil. Trans. A, vol. 374, article 20150171, 23 pages, 2016.
S11. A. Mielke. On evolutionary Γ-convergence for gradient systems. "Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity", eds. A. Muntean, J. Rademacher, A. Zagaris; proceedings of Summer School in Twente University (June 2012), Lecture Notes in Appl. Math. Mech., pp. 187-249, Springer 2016.
P56. A. Mielke. Free energy, free entropy, and a gradient structure for thermoplasticity. "Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems" in Lecture Notes in Appl. Comp. Mechanics, eds. K. Weinberg and A. Pandolfi, vol. 81, pp. 135-160, Springer 2016.
P55. A. Mielke, R. Rossi, G. Savaré. Balanced-Viscosity solutions for multi-rate systems. J. Phys., MURPHYS-HSFS Proc., eds. O. Klein et al., vol. 727 (1), article 012010, 26 pages, 2016, pdf.
P54. A. Mielke. Deriving effective models for multiscale systems via evolutionary Γ-convergence. Control of Self-Organizing Nonlinear Systems, eds. E. Schöll, S. Klapp, Ph. Hövel, pp. 235-251, Springer 2016.
2015
B8. B. Fiedler, M. Haragus, A. Mielke, G. Raugel, Y. Yi (editors). Special Issue in Memory of Klaus Kirchgässner. J. Dynam. Differential Equations, Volume 27, issues 3-4, pages 333-1171, Springer 2015.
B7. A. Mielke, T. Roubíček. Rate-Independent Systems: Theory and Application. Applied Mathematical Sciences, Volume 193, XXII+660 pages, New York: Springer 2015.
S10. A. Mielke. Variational approaches and methods for dissipative material models with multiple scales. Chapter 5 in "S. Conti, K. Hackl: Analysis and Computation of Microstructure in Finite Plasticity", Springer 2015, Lecture Notes in Appl. Comp. Mechanics, 78: 125-155.
J135. A. Mielke, J. Haskovec, P. Markowich. On uniform decay of the entropy for reaction-diffusion systems. J. Dynam. Differential Equations, 27 (3-4): 897-928, 2015.
J134. Dreyer, R. Huth, A. Mielke, J. Rehberg, M. Winkler. Global existence for a nonlocal and nonlinear Fokker-Planck equation. ZAMP, 66: 293-315, 2015.
J133. A. Mielke, J. Naumann. Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence. Comptes Rendus Acad. Sci. Paris Ser. I, 353: 321-326, 2015.
J132. A. Mielke. Deriving amplitude equations via evolutionary Γ-convergence. DCDS(A) Discrete Contin. Dyn. Syst. Ser. A, 35(6): 2679-2700, 2015.
J130. S. Yanchuk, L. Lücken, M. Wolfrum, A. Mielke. Spectrum and amplitude equations for scalar delay-differential equations with large delay. DCDS(A) Discrete Contin. Dyn. Syst. Ser. A, 35(1): 537-553, 2015.
M12. A. Mielke, G. Raugel, J. Scheurle. In Memoriam Klaus Kirchgässner. J. Dynam. Differential Equations, 27(3-4): 335-342, 2015.
P53. A. Mielke. On thermodynamical couplings of quantum mechanics and macroscopic systems. Proceedings of the QMath12 Conference: pp. 331-348, 2015.
2014
J131. A. Mielke, M.A. Peletier, D.R.M. Renger. On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Potential Analysis, 41(4): 1293-1327, 2014.
J129. A. Mielke, S. Reichelt, M. Thomas. Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. AIMS J. Networks and Heterogeneous Media, 9(2): 353-382, 2014.
J128. A. Mielke and S. Zelik. On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), XIII: 67-135, 2014.
J127. A. Mielke, Ch. Ortner, Y. Şengül. An approach to nonlinear viscoelasticity via metric gradient flow. SIAM J. Math Analysis, 46(2): 1317-1347, 2014.
P52. L. Ambrosio, A. Mielke, M.A. Peletier, G. Savaré. Variational methods for evolution. Oberwolfach Reports, 3177-3254, 2014.
P51. A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk. D2 -- Mathematics for optoelectronic devices. In "MATHEON -- Mathematics for Key Technologies" in EMS Series in Industrial and Applied Mathematics, vol. 1(1): 243-256, 2014.
P50. D. Knees, R. Kornhuber, Chr. Kraus, A. Mielke, J. Sprekels. C3 -- Phase transformation and separation in solids. In "MATHEON -- Mathematics for Key Technologies" in EMS Series in Industrial and Applied Mathematics, vol. 1(1): 189-203, 2014.
M11. V. Mehrmann, A. Mielke, F. Schmidt. D -- Electronic and photonic devices. In "MATHEON -- Mathematics for Key Technologies" in EMS Series in Industrial and Applied Mathematics, vol. 1(1): 229-232, 2014.
2013
J126. M. Liero and A. Mielke. Gradient structures and geodesic convexity for reaction-diffusion systems. Phil. Trans. Royal Soc. A., 371(2005): 20120346 (28 pages), 2013.
J125. A. Mielke. Geodesic convexity of the relative entropy in reversible Markov chains. Calc. Var. Part. Diff. Equ., 48(1): 1-31, 2013.
J124. A. Mielke and U. Stefanelli. Linearized plasticity is the evolutionary Γ-limit of finite plasticity. J. Eur. Math. Soc. (JEMS), 15(3): 923-948, 2013.
J123. A. Mielke and E. Rohan. Homogenization of elastic waves in fluid-saturated porous media using the Biot model. Math. Models Meth. Appl. Sci., 23(5): 873-916, 2013.
J122. A. Glitzky and A. Mielke. A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Z. angew. Math. Physik (ZAMP), 64(1): 29-52, 2013.
J121. A. Mielke, R. Rossi and G. Savaré. Nonsmooth analysis of doubly nonlinear evolution equations. Calc. Var. 46: 253-310, 2013.
J120. A. Mielke. Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Discrete Contin. Dyn. Syst.-S, 6(2): 479-499, 2013.
M10. A. Mielke. Luftballons im Handy-Akku. Die Welt, Eine Minute Mathematik, S. 22, 21.03.2013, English version.
M9. G. Dal Maso, A. Mielke, and U. Stefanelli. Rate-independent Evolutions. (Editorial to Special Volume of 275 pp.) Discrete Contin. Dyn. Syst.-S, 6 (1): i--ii, 2013.
S9. A. Mielke. Dissipative quantum mechanics using GENERIC, Proc. of the conference on Recent Trends in Dynamical Systems, vol. 35 of Proceedings in Mathematics & Statistics, Springer, 2013: 555-585.
P49. U. Bandelow, Th. Koprucki, K. Gärtner, A. Wilms, A. Mielke. Comprehensive mathematical modeling and simulation of semiconductor lasers. Proc. of iNOW 2013: pp. A7-A8, 2013.
2012
J119. A. Mielke, R. Rossi and G. Savaré. Variational convergence of gradient flows and rate-independent evolutions in metric spaces, Milan J. Math., 80: 381-410, 2012.
J118. K. Hackl, S. Heinz, A. Mielke. A model for the evolution of laminates in finite-strain elastoplasticity. ZAMM Z. angew. Math. Mech., 92(11-12): 888-909, 2012.
J117. A. Mielke. Emergence of rate-independent dissipation from viscous systems with wiggly energies. Contin. Mech. Thermodyn., 24(4): 591-603, 2012.
J116. A. Mielke, T. Roubíček, and M. Thomas. From damage to delamination in nonlinearly elastic materials at small strains. J. Elasticity, 109: 235-273, 2012.
J115. S. Amiranashvili, U. Bandelow and A. Mielke. Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion. Opt. Quantum Electron., 44: 241-246, 2012.
J114. S. Arnrich, A. Mielke, M.A. Peletier, G. Savaré, M. Veneroni. Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction. Calc. Var. Partial Differential Equations, 44: 419-454, 2012.
J113. S. Bartels, A. Mielke, and T. Roubíček. Quasistatic small-strain plasticity in the limit of vanishing hardening and its numerical approximation. SIAM J. Numer. Anal., 50(2): 951-976, 2012.
J112. A. Mielke. Generalized Prandtl-Ishlinskii operators arising from homogenization and dimension reduction. Physica B, 407(9): 1330-1335, 2012.
J111. A. Mielke, R. Rossi and G. Savaré. BV solutions and viscosity approximations of rate-independent systems. ESAIM Control Optim. Calc. Var., 18: 36-80, 2012.
J110. A. Mielke and L. Truskinovsky. From discrete visco-elasticity to continuum rate-independent plasticity: Rigorous results. Arch. Rational Mech. Anal., 203: 577-619, 2012.
P48. A. Mielke. Multiscale gradient systems and their amplitude equations. Oberwolfach Reports, 9(4): 3588-3591, 2012.
2011
B6. S. Bianchini, E.A. Carlen, A. Mielke, C. Villani. Nonlinear PDEs and Applications. C.I.M.E. Summer School, Cetraro, Italy 2008. Lecture Notes in Mathematics, vol. 2028, 240 pages. Eds.: L. Ambrosio, G. Savaré. Springer, Heidelberg, 2011, s. WIAS preprint 1454.
J109. M. Liero and A. Mielke. An evolutionary elastoplastic plate model derived via Γ-convergence. Math. Models Meth. Appl. Sci., 21 (9): 1961-1986, 2011.
J108. A. Mielke. Formulation of thermoelastic dissipative material behavior using GENERIC. Contin. Mech. Thermodyn., 23 (3): 233-256, 2011.
J107. A. Mielke. A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Nonlinearity, 24: 1329-1346, 2011.
J106. A. Mielke. On thermodynamically consistent models and gradient structures for thermoplasticity. GAMM Mitteilungen, 34 (1): 51-58, 2011.
J105. A. Mielke and U. Stefanelli. Weighted energy-dissipation functionals for gradient flows. ESAIM Control Optim. Calc. Var., 17: 52-85, 2011.
J104. A. Mielke. Complete-damage evolution based on energies and stresses. Special Issue "Thermomechanics and Phase Change" of Discrete Cont. Dyn. Syst. Ser. S, 4: 423-439, 2011.
S8. A. Mielke. Differential, energetic, and metric formulations for rate-independent processes. Chapter 3 in ``S. Bianchini, E.A. Carlen, A. Mielke, C. Villani: Nonlinear PDE's and Application, LNM 2028, Springer 2011'', pages 87-170.
P47. Editoren A. Mielke, F. Otto, G. Savar\'e, and U. Stefanelli. Variational Methods for Evolution. Oberwolfach Reports 8(4): 3145-3216, 2011.
P46. A. Mielke. Geometry and thermodynamics for the coupling of quantum mechanics and dissipative systems. Oberwolfach Reports 8(3): 2260-2263, 2011.
2010
J103. J. Giannoulis, A. Mielke, and Chr. Sparber. High-frequency averaging in semi-classical Hartree-type equations. Asymptot. Anal., 70: 87-100, 2010.
J102. A. Mielke, L. Paoli, A. Petrov, and U. Stefanelli. Error estimates for space-time discretizations of a rate-independent variational inequality. SIAM J. Numer. Anal., 48(5): 1625-1646, 2010
J101. A. Mielke, C. Patz. Dispersive stability of infinite dimensional Hamiltonian systems on lattices. Appl. Anal., 89(9): 1493-1512, 2010
J100. D. Knees, C. Zanini, A. Mielke. Crack growth in polyconvex materials. Physica D, 239 (2010): 1470-1484.
J99. A. Mielke, T. Roubíček, and J. Zeman. Complete damage in elastic and viscoelastic media and its energetics. Comput. Methods Appl. Mech. Engrg. 199: 1242-1253, 2010.
J98. M. Thomas, A. Mielke. Damage of nonlinearly elastic materials at small strain - Existence and regularity results. ZAMM Z. angew. Math. Mech. 90(2): 88-112, 2010.
J97. Sh. Amiranashvili, U. Bandelow, and A. Mielke. Padé approximant for refractive index and nonlocal envelope equations. Opt. Commun., 283: 480-485, 2010.
M8. A. Mielke. Mathematik für Nano- und Optoelektronik. Wissenschaft Berlin 2010, Kapitel "Mathematik und ihre Anwendungen", S. 118, Berliner Wirtschaftsgespräche.
P45. A. Mielke On an evolutionary model for complete damage based on energies and stresses. Pubblicazione IMATI-CNR, T. Roubíček and U. Stefanelli, eds., 29PV10/27/0: 23-32, 2010.
P44. A. Mielke, R. Rossi, and G. Savaré. A vanishing viscosity approach to rate-independent modeling in metric spaces. Pubblicazione IMATI-CNR, T. Roubíček and U. Stefanelli, eds., 29PV10/27/0: 33-38, 2010.
P43. A. Mielke and M. Ortiz. Microstructures in Solids: From Quantum Models to Continua, Oberwolfach Reports, 7(1): 733-798, 2010.
P41. A. Mielke, L. Paoli, A. Petrov, and U. Stefanelli. Error bounds for space-time discretizations of a 3D model for shape-memory materials, Proc. of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, K. Hackl, ed., vol. 21 of IUTAM Bookseries, Springer, 2010: 185-197.
P40. Mielke. Existence theory for finite-strain crystal plasticity with gradient regularization, Proc. of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, K. Hackl, ed., vol. 21 of IUTAM Bookseries, Springer, 2010: 171-183.
2009
J96. A. Mielke, L. Paoli, A. Petrov. On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys. SIAM J. Math. Anal., 41(4): 1388-1414, 2009.
J95. A. Mielke, R. Rossi, G. Savaré. Modeling solutions with jumps for rate-independent systems on metric spaces. Discrete Contin. Dyn. Syst. Ser. A, 25(2): 585-615, 2009.
J94. A. Mielke and T. Roubíček. Numerical approaches to rate-independent processes and applications in inelasticity. ESAIM Math. Mod. Num. Anal., 43: 399-428, 2009.
J93. A. Mainik and A. Mielke. Global existence for rate-independent gradient plasticity at finite strain. J. Nonlinear Sci., 19(3): 221-248, 2009.
J92. A. Mielke and F. Rindler. Reverse approximation of energetic solutions to rate-independent processes. Nonl. diff. Eqns. Appl. (NoDEA)., 16(1): 17-40, 2009.
J91. G. Bouchitté, A. Mielke, and T. Roubíček. A complete-damage problem at small strains. ZAMP Z. Angew. Math. Phys., 60: 205-236, 2009.
J90. S. Zelik and A. Mielke. Multi-pulse evolution and space-time chaos in dissipative systems. Mem. Amer. Math. Soc., 198 (925): 1-97, 2009.
P42. A. Mielke. Vanishing-viscosity solutions for rate-independent systems, Oberwolfach Reports, 6 (4): 3073-3076, 2009.
P39. K. Hackl, S. Heinz and A. Mielke. A model for the evolution of laminates, PAMM 9(1), 2009: 43-46, published online, DOI: 10.1002/pamm.200910012.
2008
M7. A. Mielke. Differential, energetic and metric formulations for rate-independent processes, C.I.M.E. Summer School on Nonlinear PDEs and Applications, Cetraro, June 2008.
J89. A. Mielke and U. Stefanelli. A discrete variational principle for rate-independent evolution. Advances in the Calculus of Variations, vol. 1: 399-431, 2008.
J88. J. Giannoulis, M. Herrmann, and A. Mielke. Lagrangian and Hamiltonian two-scale reduction. J. Math. Phys., vol. 49, issue 10, 103505 (2008): 1-42.
J87. D. Knees, A. Mielke, and C. Zanini. On the inviscid limit of a model for crack propagation. Math. Models Methods Appl. Sci., 18(9): 1529-1568, 2008.
J86. A. Mielke, A. Petrov, J.A.C. Martins. Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit. J. Math. Anal. Appl., 348: 1012-1020, 2008.
J85. D. Knees and A. Mielke. On the energy release rate in finite-strain elasticity. Mechanics of Adv. Mat. and Structures, 15: 421-427, 2008.
J84. A. Mielke and M. Ortiz. A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. ESAIM Control Optim. Calc. Var., 14: 494-516, 2008.
J83. J. Giannoulis, A. Mielke, and C. Sparber. Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. J. Diff. Equ., 245: 939-963, 2008.
J82. R. Rossi, A. Mielke, and G. Savaré. A metric approach to a class of doubly nonlinear evolution equations and applications. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), vol. VII (2008): 97-169.
J80. D. Knees and A. Mielke. Energy release rate for cracks in finite-strain elasticity. Math. Methods Applied Sciences, 13(5)501-528, 2008.
J79. A. Mielke, T. Roubíček, and U. Stefanelli. Γ-limits and relaxations for rate-independent evolutionary problems. Calc. Var. Part. Diff. Equ., 31: 387-416, 2008.
J78. F. Auricchio, A. Mielke and U. Stefanelli. A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Math. Models Meth. Appl. Sci., 18(1): 125-164, 2008.
J77. A. Mielke. Weak convergence methods for Hamiltonian multiscale problems. DCDS(A) Discrete Contin. Dyn. Syst. Ser. A, 20(1): 53-79, 2008.
P38. A. Mielke. Lie groups in plasticity at finite strains. Oberwolfach Reports, 5(3): 1890-1893, 2008.
P37. D. Knees, A. Mielke, and C. Zanini. On rate-independent models for crack propagation. PAMM (Proceedings in Applied Mathematics and Mechanics), 2008, 8 (1): 10213-10214.
P36. A. Mielke, L. Paoli, and A. Petrov. Existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys. PAMM (Proceedings in Applied Mathematics and Mechanics), 2008, 8 (1): 10395-10396.
P35. A. Mielke. Numerical approximation techniques for rate-independent inelasticity. Proc. of the IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media, B. D. Reddy, ed., vol. 11 of IUTAM Bookseries, Springer, 2008: 53-63.
P34. H. Gajewski, J. A. Griepentrog, A. Mielke, J. Beuthan, U. Zabarylo, O. Minet. Bildsegmentation zur Untersuchung von Streulichtbildern bei der laseroptischen Diagnose von rheumatoider Arthritis. In W. Jäger, H.-J. Krebs, editors, Mathematics - Key Technology for the Future, english version "Image Segmentation for the Investigation of Scattered-Light Images when Laser-Optically Diagnosing Rheumatoid Arthritis": 149-161, Springer 2008.
2007
J81. A. Mielke and A. Petrov. Thermally driven phase transformation in shape-memory alloys. Adv. Math. Sci. Appl, 17: 667-685, 2007.
J76. A. Mielke. A model for temperature-induced phase transformations in finite-strain elasticity. IMA J. Appl. Math., 72(5): 644-658, 2007.
J75. F. Schmid and A. Mielke. Existence results for a contact problem with varying friction coefficient and nonlinear forces. ZAMM Z. angew. Math. Mech., 87 (8-9): 616-631, 2007.
J74. A. Mielke and A. Timofte. Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. SIAM J. Math. Anal., 39 (2): 642-668, 2007.
J73. A. Mielke and S.V. Zelik. Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction-diffusion systems in Rn. J. Dynam. Differential Equations, 19(2): 333-389, 2007.
J72. A. Mielke and R. Rossi. Existence and uniqueness results for a class of rate-independent hysteresis problems. Math. Models Methods Appl. Sci., 17 (1): 81-123, 2007.
M6. J. Cagnol, B. Miara, A. Mielke, and G. Stavroulakis. State of the Art, Trends, and Directions in Smart Systems.
M5. A. Mielke. Modeling and analysis of rate-independent processes, Lipschitz Lectures, Universität Bonn, January 2007.
P33. A. Mielke. Γ-convergence for rate-independent processes with applications to damage. Oberwolfach Reports, 4(2): 1617-1620, 2007.
2006
B5. A. Mielke, editor. Analysis, Modeling, and Simulation of Multiscale Problems (Final Report of the DFG Priority Program SPP 1095), XVIII-697 pages. © Springer, September 2006.
B4. R. Helmig, A. Mielke, B. Wohlmuth, editors. Multifield Problems in Fluid and Solid Mechanics. Series Lecture Notes in Applied and Computational Mechanics, 28, XI-571 pages. © Springer, August 2006.
J71. A. Mielke and A. Timofte. Modeling and analytical study for ferroelectric materials. Mechanics of Advanced Materials and Structures, 13: 457-462, 2006.
J70. M. Kočvara, A. Mielke, and T. Roubíček. A rate-independent approach to the delamination problem. Math. Mech. Solids, 11: 423-447, 2006.
J69. A. Mielke. Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Arch. Rational Mech. Anal., 181: 401-448, 2006.
J68. G. Francfort and A. Mielke. Existence results for a class of rate-independent material models with nonconvex elastic energies. J. reine angew. Math., 595: 55-91, 2006.
J67. A. Mielke and A. Timofte. An energetic material model for time-dependent ferroelectric behavior: existence and uniqueness. Math. Meth. Appl. Sciences, 29: 1393-1410, 2006.
J65. A. Mielke and T. Roubíček. Rate-independent damage processes in nonlinear elasticity. Math. Models Methods Appl. Sci., 16: 177-209, 2006.
J64. J. Giannoulis and A. Mielke. Dispersive evolution of pulses in oscillator chains with general interaction potentials. Discr. Cont. Dynam. Systems Ser. B, 6: 493-523, 2006.
J63. A. Mielke and S. Müller. Lower semicontinuity and existence of minimizers for a functional in elastoplasticity. ZAMM Z. angew. Math. Mech., 86: 233-250, 2006.
J62. M. Efendiev and A. Mielke. On the rate-independent limit of systems with dry friction and small viscosity. J. Convex Analysis, 13: 151-167, 2006.
J61. W. Dreyer, M. Herrmann, and A. Mielke. Micro-macro transition for the atomic chain via Whitham's modulation equation. Nonlinearity, 19: 471-500, 2006.
P31. A. Mielke. Deriving modulation equations via Lagrangian and Hamiltonian reduction. Oberwolfach Reports, 3(4): 3032-3034, 2006.
P30. A. Mielke. Two-scale modeling for Hamiltonian systems: formal and rigorous results. Oberwolfach Reports, 3(4): 2656-2659, 2006.
P29. A. Mielke. Gamma convergence for evolutionary problems. Oberwolfach Reports, 3(2): 1697-1700, 2006.
P28. C. Patz, A. Mielke. Dispersive and long-time behavior of oscillations in lattices. PAMM (Proceedings in Applied Mathematics and Mechanics), DOI: 10.1002/pamm.200610232, pp. 503-504. Published online.
P27. J. Giannoulis, M. Herrmann, and A. Mielke. Continuum descriptions for the dynamics in discrete lattices: derivation and justification. In A. Mielke, editor, Analysis, Modeling, and Simulation of Multiscale Problems: Final report of the DFG Priority Program SPP 1095, pp. 435-466. Springer, 2006.
P26. E. Gürses, A. Mainik, C. Miehe, and A. Mielke. Analytical and numerical methods for finite-strain elastoplasticity. In R. Helmig, A. Mielke, B. Wohlmuth, editors, Multifield problems in Fluid and Solid Mechanics. Series Lecture Notes in Applied and Computational Mechanics, 28: 491-529. Springer, 2006.
P25. A. Mielke. A mathematical framework for standard generalized materials in the rate-independent case. In R. Helmig, A. Mielke, B. Wohlmuth, editors, Multifield problems in Fluid and Solid Mechanics. Series Lecture Notes in Applied and Computational Mechanics, 28: 399-428. Springer, 2006.
2005
J66. F. Schmid and A. Mielke. Vortex pinning in super-conductivity as a rate-independent process. Europ. J. Appl. Math. 16: 799-808, 2005. Preprint (pdf).
J60. M. Kružík, A. Mielke, and T. Roubíček. Modelling of microstructure and its evolution in shape-memory-alloy single cristals, in particular in CuAlNi. Meccanica, 40: 389-418, 2005.
J59. A. Mielke. Necessary and sufficient conditions for polyconvexity of isotropic functions. J. Convex Analysis, 12: 291-314, 2005.
J58. A. Afendikov and A. Mielke. Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip. J. Math. Fluid Mechanics, 7: S51-S67, 2005.
J57. A. Mainik and A. Mielke. Existence results for energetic models for rate-independent systems. Calc. Var. PDEs, 22: 73-99, 2005.
S7. A. Mielke. Evolution in rate-independent systems (ch. 6). In C. Dafermos and E. Feireisl, editors, Handbook of Differential Equations, Evolutionary Equations, 2: 461-559. Elsevier B.V., 2005.
P24. A. Mielke. Some existence results in finite-strain plasticity. Oberwolfach Reports, 2(4): 2991-2993, 2005.
P21. A. Mielke. Modeling and analysis of rate-independent processes in continuum mechanics. In Y. Wang and K. Hutter, editors, Trends in Applications of Mathematics to Mechanics, pp. 299-309. Shaker Verlag, 2005.
2004
J56. A. Mielke. Deriving new evolution equations for microstructures via relaxation of variational incremental problems. Comput. Methods Appl. Mech. Engrg., 193: 5095-5127, 2004.
J55. A. Mielke. Existence of minimizers in incremental elasto-plasticity with finite strains. SIAM J. Math. Analysis, 36: 384-404, 2004.
J54. A. Mielke and F. Theil. On rate-independent hysteresis models. Nonl. diff. Eqns. Appl (NoDEA), 11: 151-189, 2004.
J53. Y.B. Fu and A. Mielke. Uniqueness of the surface-wave speed: a proof that is independent of the Stroh formalism. Math. Mechanics Solids, 9: 5-15, 2004.
J52. J. Giannoulis and A. Mielke. The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities. Nonlinearity, 17: 551-565, 2004.
J51. A. Mielke. Chaos and Šarkovskiís Anordnung der natürlichen Zahlen. Mathematikinformation, 40: 48-54, 2004.
P23. A. Mielke. Energy transport in periodic lattices. Oberwolfach Reports, 1(4): 3019-3022, 2004.
P22. A. Mielke. Rate-independent models of phase transition. Oberwolfach Reports, 1(3): 1631-1634, 2004.
P20. J. Giannoulis and A. Mielke. Macroscopic pulse evolution for a nonlinear oscillator chain. PAMM Proc. Appl. Math. Mech., 4: 540-541, 2004.
P19. A. Mielke. A new approach to elasto-plasticity using energy and dissipation functionals. In J. Hill and R. Moore, editors, Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress, pp. 315-335. SIAM, 2004.
2003
J50. A. Mielke and T. Roubíček. A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul., 1: 571-597, 2003.
J49. A. Mielke. Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Cont. Mech. Thermodynamics, 15: 351-382, 2003.
J48. T. Gallay and A. Mielke. Convergence results for a coarsening model using global linearization. J. Nonlinear Science, 13: 311-346, 2003.
P18. K. Hackl, A. Mielke, and D. Mittenhuber. Dissipation distances in multiplicative elastoplasticity. In W. Wendland and M. Efendiev, editors, Analysis and Simulation of Multifield Problems, pp. 87-100. Springer-Verlag, 2003.
P17. A. Mielke. Evolution of rate-independent inelasticity with microstructure using relaxation and Young measures. In C. Miehe, editor, IUTAM Symposium on Computational Mechanics of Solid Materials at large Strains (Stuttgart August 2001), pp. 33-44, Kluwer, 2003.
2002
J47. A. Mielke and S. Zelik. Infinite-dimensional trajectory attractors for elliptic boundary-value problems on cylindrical domains. Russian Math. Surveys, 57: 753-784, 2002. Translated in Uspekhi Mat. Nauk, 57, no. 4(345): 119-150, 2002.
J46. A. Mielke. On the energetic stability of solitary water waves. Phil. Trans. Royal Soc. London, 360: 2337-2358, 2002.
J45. Y.B. Fu and A. Mielke. A new identity for the surface impedance matrix and its application to the determination of surface-wave speeds. Proc. Royal Soc. London Ser. A, 458: 2523-2543, 2002.
J44. S. Govindjee, A. Mielke, and G. Hall. The free-energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis. J. Mech. Physics Solids, 50: 1897-1922, 2002. Erratum and Correct Reprinting: 51(4) 2003, pages 763 & I-XXVI.
J43. C. Carstensen, K. Hackl, and A. Mielke. Non-convex potentials and microstructures in finite-strain plasticity. Proc. Royal Soc. London, Ser. A, 458: 299-317, 2002.
J42. A. Mielke, F. Theil, and V.I. Levitas. A variational formulation of rate-independent phase transformations using an extremum principle. Arch. Rational Mech. Anal., 162: 137-177, 2002. Essential Science Indicator: Emerging Research Fronts Paper in Mathematics in August 2006.
S6. A. Mielke. Analysis of energetic models for rate-independent materials. In T. Li, editor, Proceedings of the Int. Congress of Mathematicians 2002, Beijing, III: 817-828. Higher Education Press, 2002.
S5. A. Mielke. Finite elastoplasticity, Lie groups and geodesics on SL(d). In P. Newton, A. Weinstein, and P.J. Holmes, editors, Geometry, Dynamics, and Mechanics, pp. 61-90. Springer-Verlag, 2002.
S4. A. Mielke. The Ginzburg-Landau equation in its role as a modulation equation. In B. Fiedler, editor, Handbook of Dynamical Systems II, pp. 759-834. Elsevier Science B.V., 2002.
M4. A. Mielke. Relaxation via Young measures of material models for rate-independent inelasticity. Stuttgart, 2002.
2001
J41. A. Afendikov and A. Mielke. Nonlocal modulation equations for viscous fluid layer problems and persistence of spatially localized pertrubations. Dokl. Akad. Nauk, 381(4): 479-483, 2001. Translated in Doklady Physics 46(12): 869-872, 2001.
J40. B. Buffoni and A. Mielke. On interfaces between incompatible wells and elastic deformations of infinite cylinders. Calc. Var. PDEs, 13: 469-489, 2001.
J39. A. Afendikov and A. Mielke. Multi-pulse solutions to the Navier-Stokes problem between parallel plates. Z. angew. Math. Phys., 52(1): 79-100, 2001.
J38. M. Groves and A. Mielke. A spatial dynamics approach to three-dimensional gravity-capillary steady water waves. Proc. Roy. Soc. Edinburgh Sect. A, 131: 83-136, 2001. Essential Science Indicator: Fast Breaking Paper in Mathematics in April 2003.
S3. A. Mielke, G. Schneider, and H. Uecker. Stability and diffusive dynamics on extended domains. In B. Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pp. 563-583. Springer-Verlag, 2001.
2000
J37. A. Mielke, G. Schneider, and A. Ziegra. Comparison of inertial manifolds and application to modulated systems. Math. Nachr., 214: 53-69, 2000.
J36. M.S. Kuczma and A. Mielke. Influence of hardening and inhomogeneity on internal loops in pseudoelasticity. ZAMM Z. Angew. Math. Mech., 80(5): 291-306, 2000.
S2. A. Mielke. Mathematical analysis of sideband instabilities with application to Rayleigh-Bénard convection. In Mechanics: from theory to computation, pp. 335-377. Springer, New York, 2000.
P16. A. Mielke. Estimates on the mixture function for multiphase problems in elasticity. In A.-M. Sändig, W. Schiehlen, and W. Wendland, editors, Multifield problems, pp. 96-103, Berlin, 2000. Springer-Verlag.
P15. A. Mielke. Exponentially weighed L-estimates and attractors for parabolic systems on unbounded domains. In B. Fiedler, K. Gröger, and J. Sprekels, editors, International Conference on Differential Equations (Equadiff 99) Berlin 1999, vol. I, pp. 641-646. World Scientific, 2000.
P14. A. Mielke. Pattern formation on large domains and diffusive mixing. In G. Iooss, O. Guès, and A. Nouri, editors, Trends in applications of mathematics to mechanics (Nice, 1998), STAMM X, pp. 228-237. Chapman & Hall/CRC, Boca Raton, FL, 2000.
P13. A. Afendikov and A. Mielke. Multipulse solutions in problems with reflection symmetry in cylindrical domains. In. B. Fiedler, K. Gröger, and J. Sprekels, editors, International Conference on Differential Equations (Equadiff 99) Berlin 1999, vol. I, pp. 769-771. World Scientific, 2000.
1999
J35. M.S. Kuczma, A. Mielke, and E. Stein. Modelling of hysteresis in two-phase systems. Archive of Mechanics (Warzawa), 51: 693-715, 1999.
J34. A. Afendikov and A. Mielke. Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2) symmetry. J. diff. Eqns, 159: 370-402, 1999.
J33. A. Afendikov and A. Mielke. On families of reversible SO(2)-invariant vector fields with a non-semi-simple zero eigenvalue of multiplicity four. Dokl. Akad. Nauk, 369(2): 153-157, 1999. English translation: Doklady Mathematics 60: 332-336, 1999.
J32. A. Mielke. Flow properties for Young-measure solutions of semilinear hyperbolic problems. Proc. Roy. Soc. Edinburgh Sect. A, 129: 85-123, 1999.
P12. A. Mielke and F. Theil. A mathematical model for rate-independent phase transformations with hysteresis. In H.-D. Alber, R. Balean, and R. Farwig, editors, Proceedings of the Workshop on Models of Continuum Mechanics in Analysis and Engineering, pp. 117-129. Shaker-Verlag, 1999.
1998
J31. T. Gallay and A. Mielke. Diffusive mixing of stable states in the Ginzburg-Landau equation. Comm. Math. Phys., 199(1): 71-97, 1998.
J30. A. Mielke, P.J. Holmes, and J.N. Kutz. Global existence and uniqueness for an optical fibre laser model. Nonlinearity, 11: 1489-1504, 1998.
J29. A. Mielke and P. Sprenger. Quasiconvexity at the boundary and a simple variational formulation of Agmon's condition. J. Elasticity, 51: 23-41, 1998.
J28. A. Mielke. Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Phys. D, 117: 106-116, 1998.
M3. A. Mielke, F. Theil, and V.I. Levitas. Mathematical formulation of quasistatic phase transformations with friction using an extremum principle. Hannover, 1998.
1997
J27. A. Mielke. Instability and stability of rolls in the Swift-Hohenberg equation. Comm. Math. Phys., 189: 829-853, 1997.
J26. A. Mielke. The complex Ginzburg-Landau equation on large and unbounded domains: sharper bounds and attractors. Nonlinearity, 10: 199-222, 1997.
J25. A. Mielke. Mathematical analysis of sideband instabilities with application to Reyleigh-Bénard convection. J. Nonlinear Sci., 7: 57-99, 1997.
P11. A. Mielke and P. Sprenger. Homogeneous deformations as global minimizers in nonlinear elasticity. In ZAMM Z. angew. Math. Mech. (Suppl. 2), 77: S683-684, 1997.
P10. M.S. Kuczma, V.I. Levitas, A. Mielke, and E. Stein. Nonisothermal hysteresis loops in pseudoelasticity. In A. Garstecki and J. Rakowski, editors, Proc. XIII Polish Conf. on Computer Methods in Mechanics, Poznan, May 5-9, 1997, II: 711-718, 1997.
P9. M.S. Kuczma and A. Mielke. Variational approach to pseudoelastic behaviour. In ZAMM Z. angew. Math. Mech. (Suppl. 1), 77: S176-177, 1997.
1996
B3. G. Dangelmayr, B. Fiedler, K. Kirchgässner, and A. Mielke, editors. Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifucation and Stability. Pitman Research Notes in Mathematics Series, Vol. 352, 277 pages. Longman, Harlow, 1996. With contribution by G. Raugel.
S1. A. Mielke and G. Schneider. Derivation and justification of the complext Ginzburg-Landau equation as a modulation equation. In. P. Deift, C. Levermore, and C. Wayne, editors. Dynamical systems and probabilistic methods in partial differential equations (Berkeley, CA, 1994), pp. 191-216. Amer. Math. Soc., Providence, RI, 1996.
J24. T. Bridges and A. Mielke. Instability of spatially-periodic states for a family of semilinear PDE's on an infinite strip. Math. Nachr., 179: 5-25, 1996.
1995
B2. A. Mielke and K. Kirchgässner, editors. Structure and Dynamics of Nonlinear Waves in Fluids. Proceedings of the IUTAM/ISIMM Symposium held in Hannover, August 17-20, 1994. World Scientific Publishing Co. Inc., Singapore, 1995.
J23. T. Bridges and A. Mielke. A proof of the Banjamin-Feir instability. Arch. Rational Mech. Anal., 133: 145-198, 1995.
J22. A. Mielke and G. Schneider. Attractors for modulation equations on unbounded domains - existence and comparison. Nonlinearity, 8: 743-768, 1995.
J21. A. Mielke. On the justification of plate theories in linear elasticity theory using exponential decay estimates. J. Elasticity, 38: 165-208, 1995.
J20. A. Afendikov and A. Mielke. Bifurcations of Poiseuille flow between parallel plates: three-dimensional solutions with large spanwise wavelength. Arch. Rational Mech. Anal., 129(2): 101-127, 1995.
P8. A. Mielke. A new approach to sideband-instabilities using the principle of reduced instability. In A. Doelman and A. van Harten, editors, Nonlinear dynamics and pattern formation in the natural enviroment (Noordwijkerhout, 1994), pp. 206-222, Harlow, 1995. Longman.
P7. A. Mielke. Homoclinic and heteroclinic solutions in two-phase flow. In A. Mielke and K. Kirchgässner, editors. Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids (Hannover, 1994), pp. 353-362. World Sci. Publishing, 1995.
P6. A. Afendikov and A. Mielke. Instability of standing waves in large wavelength in problems with O(2) symmetry. In A. Mielke and K. Kirchgässner, editors. Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids (Hannover, 1994), pp. 133-138, River Edge, NJ, 1995. World Sci. Publishing.
1994
J19. A. Mielke. Floquet theory for, and bifurcations from spatially periodic patterns. Tatra Mt. Math. Publ., 4: 153-158, 1994. Equadiff 8 (Bratislava, 1993).
J18. A. Mielke. Essential manifolds for an elliptic problem in an infinite strip. J. Differential Equations, 110: 322-355, 1994.
P5. A. Afendikov and A. Mielke. A spatial center manifold approach to a hydrodynamical problem with O(2) symmetry. In P. Chossat, editor, Dynamics, Bifurcation and Symmetry (Cargèse, 1993), pp. 1-10, Dordrecht, 1994. Kluwer Acad. Publ.
1992
J17. A. Mielke. On nonlinear problems of mixed type: a qualitative theory using infinite-dimensional center manifolds. J. Dynam. Differential Equations, 4: 419-443, 1992.
J16. P. Kirrmann, G. Schneider, and A. Mielke. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A, 122: 85-91, 1992.
J15. A. Mielke. Reduction of PDEs on domains with several unbounded directions: a first step towards modulation equations. Z. angew. Math, Phys., 43(3): 449-470, 1992
J14. G. Iooss and A. Mielke. Time-periodic Ginzburg-Landau equations for one-dimensional patterns with large wave length. Z. angew. Math. Phys., 43(1): 125-138, 1992.
J13. A. Mielke, P. Holmes, and O. O'Reilly. Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center. J. Dynam. Differential Equations, 4(1): 95-126, 1992.
1991
B1. A. Mielke. Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems. Lecture Notes in Mathematics Vol. 1489, Springer-Verlag 1991 (vii + 140 pages).
J12. A. Mielke. Locally invariant manifolds for quasilinear parabolic equations. Rocky Mountain J. Math., 21: 707-714, 1991. Current directions in nonlinear partial differential equations (Provo, UT, 1987).
J11. G. Iooss and A. Mielke. Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders. J. Nonlinear Sci., 1(1): 107-146, 1991.
P4. G. Iooss and A. Mielke. Hydrodynamical stability problems in infinitely long cylindrical domains: existence of defects in travelling waves. In S. Rionero, editor, Waves and stability in continuous media (Sorrento, 1989), pp. 243-257. World Sci. Publishing, River Edge, NJ, 1991.
P3. G. Iooss and A. Mielke. Reduction and normalization of hydrodynamical stability problems in infinitely long cylinders. In W. Schneider, H. Troger, and F. Ziegler, editors, Trends in Applications of Mathematics to Mechanics (Hollabrunn, 1989) STAMM VIII, pp. 43-56. Longman Sci. Tech., Harlow, 1991.
1990
J10. A. Mielke. Topological methods for discrete dynamical systems. Mitt. Ges. Angew. Math. Mech., 90/2: 19-37, 1990.
J9. A. Mielke. Normal hyperbolicity of center manifolds and Saint-Vernant's principle. Arch. Rational Mech. Anal., 110: 353-372, 1990.
P2. G. Iooss, A. Mielke, and Y. Demay. Mathematical justification of steady Ginzburg-Landau equation starting from Navier-Stokes. In New trends in nonlinear dynamics and pattern-forming phenomena (Cargèse, 1988), pp. 275-286. Plenum, New York, 1990.
M2. A. Mielke. Hamiltonische und Lagrangesche Flüsse auf Zentrumsmannigfaltigkeiten mit Anwendungen auf elliptische Variationsprobleme. Fakultät Mathematik, Universität Stuttgart, 1990.
1989
J8. G. Iooss, A. Mielke, and Y. Demay. Theory of steady Ginzburg-Landau equation in hydrodynamic stability problems. European J. Mech. B Fluids, 8(3): 229-268, 1989.
1988
J7. A. Mielke. Saint-Vernant's problem and semi-inverse solutions in nonlinear elasticity. Arch. Rational Mech. Anal., 102: 205-229, 1988. Corrigendum in 110 (1990): 351-352.
J6. A. Mielke. On Saint-Vernant's problem for an elastic strip. Proc. Roy. Soc. Edinburgh Sect. A, 110: 161-181, 1988.
J5. A. Mielke and P.J. Holmes. Spatially complex equilibria of buckled rods. Arch. Rational Mech. Anal., 101: 319-348, 1988.
J4. A. Mielke. Reduction of quasilinear elliptic equations in cylindrical domains with applications. Math. Methods Appl. Sci., 10: 51-66, 1988.
P1. A. Mielke. On Saint-Vernant's problem and Saint-Vernant's principle in nonlinear elasticity. In J. Besseling and W. Eckhaus, editors, Trends in Applications of Mathematics to Mechanics (Wassenaar, 1987), STAMM VII, pp. 252-260. Springer, Berlin, 1988.
1987
J3. A. Mielke. Über maximale Lp-Regularität für Differentialgleichungen in Banach- und Hilbert-Räumen. Math. Ann., 277: 121-133, 1987.
1986
J2. A. Mielke. Steady flows of inviscid fluids under localized perturbations. J. Diff. Equations, 65: 89-116, 1986.
J1. A. Mielke. A reduction principle for nonautonomous systems in infinite-dimensional spaces. J. Diff. Equations, 65: 68-88, 1986.
1984
M1. A. Mielke. Stationäre Lösungen der Euler-Gleichung in Kanälen variabler Tiefe. Fakultät Mathematik, Universität Stuttgart, July 1984