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Heinemann, Christian; Kraus, Christiane

Existence results for diffuse interface models describing phase separation and damage. (English) Zbl 1290.35265

Eur. J. Appl. Math. 24, No. 2, 179-211 (2013).
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.
Reviewer: Thomas Ernst (Uppsala)

Cited in 14 Documents

MSC:

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

Keywords:

Cahn-Hilliard systems; Allen-Cahn systems; phase separation; damage; elliptic-parabolic systems; energetic solution; weak solution; doubly nonlinear differential inclusions; existence results; rate-dependent systems; logarithmic-free energy
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\textit{C. Heinemann} and \textit{C. Kraus}, Eur. J. Appl. Math. 24, No. 2, 179--211 (2013; Zbl 1290.35265)
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