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arXiv · 1502.05861

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

Christian Heinemann·Christiane Kraus
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Abstract

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.

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Christian Heinemann, Christiane Kraus. 2015-02-20. Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects. https://doi.org/10.3934/dcds.2015.35.2565

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