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

Christian Heinemann; Christiane Kraus

doi:10.3934/dcds.2015.35.2565

Article Contents

2015, Volume 35, Issue 6: 2565-2590. Doi: 10.3934/dcds.2015.35.2565

This issue Previous Article Robust exponential attractors for the modified phase-field crystal equation Next Article On the representation of hysteresis operators acting on vector-valued, left-continuous and piecewise monotaffine and continuous functions

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

Christian Heinemann^1, and
Christiane Kraus^1,

1.
Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117 Berlin

Received: December 2013

Revised: February 2014

Published online: December 2014

Abstract / Introduction Related Papers Cited by

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 [12]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques.

Keywords:

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

Mathematics Subject Classification: 35L20, 35L51, 35K86, 35K55, 49J40, 49S05, 74A45, 74G25, 34A12, 82B26, 82C26, 35K92, 35K35.

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