WIAS Preprint No. 1919, (2014)

Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects


  • Heinemann, Christian
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 35L20 35L51 35K85 35K55 49J40 49S05 74A45 74G25 34A12 82B26 82C26 35K92 35K35


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


In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first adopt the notion of weak solutions introduced in [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321-359]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques.

Appeared in

  • Discrete Contin. Dyn. Syst., 35 (2015) pp. 2565--2590.

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