Christian Heinemann, Christiane Kraus, Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, e-mail: christian.heinemann@wias-berlin.de, christiane.kraus@wias-berlin.de
Abstract: This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent domain which characterizes the nondegenerated elastic material regions. We choose a notion of weak solutions which consists of weak formulations of the Cahn-Hilliard system and the momentum balance equation, a variational inequality for the damage evolution and an energy inequality. For the introduced degenerating system, we prove global-in-time existence of weak solutions. The main results are sketched from our recent paper [WIAS preprint no. 1759 (2012)].
Keywords: Cahn-Hilliard system; phase separation; complete damage; elliptic-parabolic degenerating system; linear elasticity; energetic solution; weak solution; doubly nonlinear differential inclusion; existence result; rate-dependent system
Classification (MSC 2010): 35K85, 35K55, 49S05, 35J50, 74A45, 74G25, 34A12, 82B26, 35K92, 35K65
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