Existence of weak solutions fora PDE system describing phase separation and damage processes including inertial effects
Christian Heinemann, Christiane Kraus · Discrete and Continuous Dynamical Systems · 2015
In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloysin the presence of inertial effects.The material is considered on a bounded Lipschitz domain with mixedboundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for theintroduced hyperbolic-parabolic system. To this end,we first adopt the notion of weak solutions introducedin [12]. Then weprove existence of weak solutions by means of regularization, time-discretizationand different variational techniques.