WIAS Preprint No. 1569, (2010)

Existence results for diffuse interface models describing phase separation and damage



Authors

  • Heinemann, Christian
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 35K85 49J40 49S05 74C10 82C26 35J50 35K35 35K55

2008 Physics and Astronomy Classification Scheme

  • 02.30.Jr

Keywords

  • Cahn-Hilliard systems, Allen-Cahn systems, logarithmic free energy, phase separation, damage, elliptic-parabolic systems, energetic solution, weak solution, doubly nonlinear, differential inclusions, existence results, rate-dependent systems

Abstract

In this paper we analytically investigate Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. We are interested in the case where the free energy contains logarithmic terms of the chemical concentration variable and quadratic terms of the gradient of the damage variable. For elastic Cahn-Hilliard and Allen-Cahn systems coupled with uni-directional damage processes, an appropriate notion of weak solutions is presented as well as an existence result based on certain regularization methods and an higher integrability result for the strain.

Appeared in

  • European J. Appl. Math., 24 (2013) pp. 179--211.

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