@Article{JPDE-30-2,
author = {Kraus, Christiane and Roggensack, Arne},
title = {Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage.},
journal = {Journal of Partial Differential Equations},
year = {2017},
volume = {30},
number = {2},
pages = {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.},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v30.n2.2},
url = {https://global-sci.com/article/88227/existence-of-weak-solutions-for-the-cahn-hilliard-reaction-model-including-elastic-effects-and-damage}
}