WIAS Preprint No. 2123, (2015)

Coupling rate-independent and rate-dependent processes: Existence results


  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X

2010 Mathematics Subject Classification

  • 35A15 35A23 35A35 35G61 49J53 35Q74 74H20 74C05 74C10


  • Rate-independent processes, gradient systems, inertia, energetic solutions, existence results, time-discretization, generalized standard solids




We address the analysis of an abstract system coupling a rate-independet process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.

Appeared in

  • SIAM J. Math. Anal., 49 (2017), pp. 1419--1494.

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