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Existence of weak solutions for the Cahn-Hilliard reaction model including elastic effects and damage

Please always quote using this URN:urn:nbn:de:0296-matheon-13750
  • 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 lithium-ion batteries. Mathematically, this is realized by a Cahn-Larché system with 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 of the coupled PDE system.

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Metadaten
Author:Christiane Kraus, Arne Roggensack
URN:urn:nbn:de:0296-matheon-13750
Referee:Caren Tischendorf
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/04/01
Release Date:2016/04/01
Tag:Cahn-Hilliard reaction system; doubly non-linear differential inclusion; existence; non-linear Newton boundary condition; phase separation; rate-dependent damage
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Project:C Energy and Materials (Production) / C-SE4 Mathematical modeling, analysis and novel numerical concepts for anisotropic nanostructured materials
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Dxx Generalized solutions / 35D30 Weak solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J40 Variational methods including variational inequalities [See also 47J20]
Preprint Number:1106
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