Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Cahn-Hilliard reaction system rate-dependent damage phase separation existence non-linear Newton boundary condition
• 年，卷（期）: 2017,（2）
• 页码范围: 111-145
• 页数: 35页
• 分类号: O175.29
• 语种: 英文
• DOI: 10.4208/jpde.v30.n2.2

摘要

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 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.