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

Title:

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

Creator:

Heinemann, Christian and Kraus, Christiane

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:534a9f73-b8cf-41d4-8ccf-19d8b7d54c48
uuid:534a9f73-b8cf-41d4-8ccf-19d8b7d54c48
doi:10.21136/MB.2014.143857

Subject:

Cahn-Hilliard system, phase separation, complete damage, elliptic-parabolic degenerating system, linear elasticity, energetic solution, weak solution, doubly nonlinear differential inclusion, and existence result; rate-dependent system

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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)].

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

315-331

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false