Geodesic
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 315-331

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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)].
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)].
DOI : 10.21136/MB.2014.143857
Classification : 34A12, 35A01, 35D30, 35J50, 35K55, 35K65, 35K85, 35K92, 35M30, 49S05, 74A45, 74G25, 82B26
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 
Heinemann, Christian; Kraus, Christiane. Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 315-331. doi: 10.21136/MB.2014.143857
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