The Cahn-Hilliard equation with a nonlinear source term

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:294

Article

Miranville, Alain^1,2,3 

[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang, Henan, Peoples R China

[2] Univ Poitiers, Lab I3M, UMR, CNRS 7348,Equipe DACTIM MIS, Site Futuroscope Teleport 2, F-86073 Poitiers 9, France

[3] Univ Poitiers, Lab Math & Applicat, UMR, CNRS 7348,Equipe DACTIM MIS, Site Futuroscope Teleport 2, F-86073 Poitiers 9, France

关键词: Cahn-Hilliard equation;    Nonlinear source term;    Logarithmic nonlinear term;    Existence of solutions;    Applications;   

DOI  :  10.1016/j.jde.2021.05.045

来源: Elsevier

【 摘 要 】

Our aim in this paper is to prove the existence of solutions to the Cahn-Hilliard equation with a general nonlinear source term. An essential difficulty is to obtain a global in time solution. Indeed, due to the presence of the source term, one cannot exclude the possibility of blow up in finite time when considering regular nonlinear terms and when considering an approximated scheme. Considering instead logarithmic nonlinear terms, we give sufficient conditions on the source term which ensure the existence of a global in time weak solution. These conditions are satisfied by several important models and applications which can be found in the literature. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free