WIAS Preprint No. 1841, (2013)

Modeling and analysis of a phase field system for damage and phase separation processes in solids


  • Bonetti, Elena
  • Heinemann, Christian
  • Kraus, Christiane
  • Segatti, Antonio

2010 Mathematics Subject Classification

  • 35K55 74G25 74A45


  • Cahn-Hilliard system, phase separation, elliptic-parabolic systems, doubly nonlinear differential inclusions, complete damage, existence results, energetic solutions, weak solutions, linear elasticity, rate-dependent systems




In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function. The main aim of this paper is to show existence of weak solutions for the introduced model, where, in contrast to existing damage models in the literature, different elastic properties of damaged and undamaged material are regarded. To prove existence of weak solutions for the introduced system, we start with a regularized version. Then, by passing to the limit, existence results of weak solutions for the proposed model are obtained via suitable variational techniques.

Appeared in

  • J. Partial Differ. Equ., 258 (2015) pp. 3928--3959.

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