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

Abstract

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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)].

How to cite

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Heinemann, 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 -

References

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