|
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.
|
|
2011 |
| 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.
|
| 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.
|
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.
|
|
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, issue 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. MFO Workshop on
Applied Dynamics and Geometric Mechanics, 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. MFO Workshop on Phase Transitions, 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. |
| P32. |
A. Mielke. Deriving
modulation equations via Lagrangian and Hamiltonian reduction. MFO Workshop
on Mathematical Theory of Water Waves,
Oberwolfach Reports,
3(4):
3032-3034, 2006. |
| P31. |
A. Mielke. Two-scale
modeling for Hamiltonian systems: formal and rigorous results. MFO Workshop
on PDE and
Materials,
Oberwolfach Reports, 3(4):
2656-2659, 2006. |
| P30. |
A. Mielke. Gamma
convergence for evolutionary problems. MFO Workshop on Applications of Asymptotic Analysis, Oberwolfach Reports, 3(2): 1697-1700, 2006.
|
| P29. |
A. Timofte, A. Mielke. Homogenization for rate-independent systems. PAMM (Proceedings in
Applied Mathematics and Mechanics), DOI: 10.1002/pamm.200610237, pages
513-514. Published
online. |
| 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, pages
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, pages 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, volume 2, pages 461-559. Elsevier B.V., 2005. |
| P24. |
A. Mielke. Some existence results in finite-strain
plasticity. MFO Mini-Workshop on Analysis and Computation of
Microstructures in Finite 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, pages 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. MFO
Workshop on Thermodynamische Materialtheorien,
Oberwolfach Reports, 1(4): 3019-3022, 2004. |
| P22. |
A. Mielke. Rate-independent models of phase transition. MFO
Workshop on Phasenübergänge,
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, pages 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, pages
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), pages 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, volume 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, volume III, pages 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, pages 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, pages
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, pages
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, pages 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, pages 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, volume I, pages 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, pages
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, volume I, pages 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, pages
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), volume 77, pages 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, volume II, pages 711-718, 1997. |
| P9. |
M.S. Kuczma and A. Mielke. Variational approach to pseudoelastic
behaviour. In ZAMM Z. angew. Math. Mech. (Suppl. 1), volume 77, pages
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), pages
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), pages 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), pages 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), pages 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), pages 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), pages 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, pages 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),
pages 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, pages 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 |
