WIAS Preprint No. 1890, (2013)

Existence of weak solutions for a hyperbolic-parabolic phase field system with mixed boundary conditions on non-smooth domains



Authors

  • Heinemann, Christian
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 35L20 35L51 35K85 35K55 49J40 49S05 74A45 74G25 34A12 35K92 35K35

Keywords

  • hyperbolic-parabolic systems, doubly nonlinear differential inclusions, existence results, energetic solutions, weak solutions, linear elasticity, rate-dependent systems

Abstract

The aim of this paper is to prove existence of weak solutions of hyperbolic-parabolic evolution inclusions defined on Lipschitz domains with mixed boundary conditions describing, for instance, damage processes and elasticity with inertia terms. To this end, a suitable weak formulation to deal with such evolution inclusions in a non-smooth setting is presented. Then, existence of weak solutions is proven by utilizing time-discretization, regularization of the displacement variable and variational techniques from [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321-359] to recover the subgradients after the limit passages.

Appeared in

  • SIAM J. Math. Anal., 47 (2015) pp. 2044--2073.

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