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

2015/02/20 by Heinemann, Christian, Kraus, Christiane
#34A12 #35K35 #35K55 #35K85 #35K92 #35L20 #35L51 #49J40 #49S05 #74A45 #74G25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.05856

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, H²-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.

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