Volume 30, Issue 2
Existence of Weak Solutions for the Cahn-Hilliard Reaction Model Including Elastic Effects and Damage.

Christiane Kraus & Arne Roggensack

J. Part. Diff. Eq., 30 (2017), pp. 111-145.

Published online: 2017-05

Preview Purchase PDF 80 1162
Export citation
  • 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.

  • Keywords

Cahn-Hilliard reaction system rate-dependent damage phase separation existence non-linear Newton boundary condition

  • AMS Subject Headings

35K61, 35K86, 49J40, 35D30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

christiane.kraus@wias-berlin.de (Christiane Kraus)

arne.roggensack@wias-berlin.de (Arne Roggensack)

  • BibTex
  • RIS
  • TXT
@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
Copy to clipboard
The citation has been copied to your clipboard