In this talk, we will investigate a PDE system which couples phase separation,
elasticity and damage processes.
The system is considered on a Lipschitz domain with mixed boundary conditions for
the elastic deformations.
 We will introduce a suitable notion of weak solutions consisting of weak
formulations of the diffusion and the
 momentum balance equation, a variational inequality for the damage process and an
energy inequality.
 The main aim is to prove existence of weak solutions and to investigate the
degenerate limit
 where complete damage may occur. This is a joint work with Christiane Kraus.