  In this work, we analytically investigate a multi-component system for
describing phase separation and damage processes in solids. The model consists
of a parabolic diffusion equation of fourth order for the concentration coupled
with an elliptic system with material dependent coefficients for the strain
tensor and a doubly nonlinear differential inclusion for the damage function.
The main aim of this paper is to show existence of weak solutions for the
introduced model, where, in contrast to existing damage models in the
literature, different elastic properties of damaged and undamaged material are
regarded. To prove existence of weak solutions for the introduced model, we
start with an approximation system. Then, by passing to the limit, existence
results of weak solutions for the proposed model are obtained via suitable
variational techniques.
