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Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage.
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@Article{JPDE-30-111,
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 = {http://global-sci.org/intro/article_detail/jpde/10002.html}
}
TY - JOUR
T1 - Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage.
AU - Kraus , Christiane
AU - Roggensack , Arne
JO - Journal of Partial Differential Equations
VL - 2
SP - 111
EP - 145
PY - 2017
DA - 2017/05
SN - 30
DO - http://doi.org/10.4208/jpde.v30.n2.2
UR - https://global-sci.org/intro/article_detail/jpde/10002.html
KW - Cahn-Hilliard reaction system
KW - rate-dependent damage
KW - phase separation
KW - existence
KW - non-linear Newton boundary condition
AB - 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.
Christiane Kraus & Arne Roggensack. (2019). Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage..
Journal of Partial Differential Equations. 30 (2).
111-145.
doi:10.4208/jpde.v30.n2.2
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