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

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 inertial effects. To this end, we first present a suitable weak formulation in order to deal with such evolution inclusions. Then, existence of weak solutions is proven by utilizing time-discretization, H2-regularization and variational techniques.