Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage.
Year: 2017
Author: Christiane Kraus, Arne Roggensack
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 111–145
Abstract
In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of batteries. Mathematically, this is realized by a Cahn-Larch systemwith a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n2.2
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 111–145
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Cahn-Hilliard reaction system