Existence of weak solutions for a hyperbolic-parabolic phase field system with mixed boundary conditions on non-smooth domains
Analysis of PDEs
2016-09-16 v2
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.
Keywords
Cite
@article{arxiv.1502.05856,
title = {Existence of weak solutions for a hyperbolic-parabolic phase field system with mixed boundary conditions on non-smooth domains},
author = {Christian Heinemann and Christiane Kraus},
journal= {arXiv preprint arXiv:1502.05856},
year = {2016}
}