Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Marin-Rubio, Pedro¹  Planas, Gabriela²  Real, Jose¹ 

[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, E-41080 Seville, Spain

[2] Univ Estadual Campinas, Dept Matemat, Inst Matemat Estatist & Computacao Cient, BR-13083859 Campinas, SP, Brazil

关键词: Phase-field model;    Multi-valued dynamical systems;    Global attractors;   

DOI  :  10.1016/j.jde.2009.01.021

来源: Elsevier

【 摘 要 】

We prove the existence of weak solutions for a phase-field model with three coupled equations with unknown uniqueness, and state several dynamical systems depending on the regularity of the initial data. Then, the existence of families of global attractors (level-set depending) for the corresponding multi-valued semiflows is established, applying an energy method. Finally, using the regularizing effect of the problem, we prove that these attractors are in fact the same. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free