# Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

Christian Heinemann; Christiane Kraus

Mathematica Bohemica (2014)

- Volume: 139, Issue: 2, page 315-331
- ISSN: 0862-7959

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topHeinemann, Christian, and Kraus, Christiane. "Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes." Mathematica Bohemica 139.2 (2014): 315-331. <http://eudml.org/doc/261883>.

@article{Heinemann2014,

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)].},

author = {Heinemann, Christian, Kraus, Christiane},

journal = {Mathematica Bohemica},

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; 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},

language = {eng},

number = {2},

pages = {315-331},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes},

url = {http://eudml.org/doc/261883},

volume = {139},

year = {2014},

}

TY - JOUR

AU - Heinemann, Christian

AU - Kraus, Christiane

TI - Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

JO - Mathematica Bohemica

PY - 2014

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 139

IS - 2

SP - 315

EP - 331

AB - 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)].

LA - eng

KW - 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; 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

UR - http://eudml.org/doc/261883

ER -

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