Cahn-Hilliard systems coupled with complete damage processes and homogeneous elasticity

Abstract

This chapter combines the approach from Chapter 4 with the ideas from the preceding chapter. More specifically, we are going to investigate existence of weak solutions for complete damage systems which are coupled with degenerating Cahn-Hilliard equations. The diffusion mobility tensor depends on the damage variable and vanishes when the damage is maximal. Therefore, we have two degenerating terms in the resulting system: the elastic energy density and the mobility tensor.