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Existence results for diffuse interface models describing phase separation and damage. (English) Zbl 1290.35265
The authors investigate multi-component Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. After the introduction of notation and labeling of the two systems of four equations \(S_0\) and \(S_c\), an appropriate notion of weak solutions is presented. Then existence of weak solutions for \(S_0\) (two cases) and \(S_c\) is shown, together with higher integrability of the strain tensor.

MSC:
35Q74 PDEs in connection with mechanics of deformable solids
35D30 Weak solutions to PDEs
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