Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness |
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| Authors: | Pedro Marín-Rubio Gabriela Planas |
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| Institution: | a Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080 Sevilla, Spain
b Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-859 Campinas, SP, Brazil |
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| Abstract: | 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. |
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| Keywords: | 35B41 35K55 35K65 80A22 |
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