WIAS Preprint No. 1520, (2010)

Existence of weak solutions for Cahn--Hilliard systems coupled with elasticity and damage


  • Heinemann, Christian
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 35K85 82C26 35K55


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




A typical phase field approach for describing phase separation and coarsening phenomena in alloys is the Cahn-Hilliard model. This model has been generalized to the so-called Cahn-Larché system by combining it with elasticity to capture non-neglecting deformation phenomena, which occur during phase separation and coarsening processes in the material. In order to account for damage effects, we extend the existing framework of Cahn-Hilliard and Cahn-Larché systems by incorporating an internal damage variable of local character. This damage variable allows to model the effect that damage of a material point is influenced by its local surrounding. The damage process is described by a unidirectional rate-dependent evolution inclusion for the internal variable. For the introduced Cahn-Larché systems coupled with rate-dependent damage processes, we establish a suitable notion of weak solutions and prove existence of weak solutions.

Appeared in

  • Adv. Math. Sci. Appl., 21 (2011) pp. 321--359.

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