Global Attractor and Omega-Limit Sets Structure for a Phase-Field Model of Thermal Alloys

In this paper, the existence of weak solutions is established for a phase-field model of thermal alloys supplemented with Dirichlet boundary conditions. After that, the existence of global attractors for the associated multi-valued dynamical systems is proved, and the relationship among these sets i...

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Detalles Bibliográficos
Autores: Planas, Gabriela, Marín Rubio, Pedro
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25930
Acceso en línea:http://hdl.handle.net/11441/25930
https://doi.org/10.1016/j.nonrwa.2011.11.024
Access Level:acceso abierto
Palabra clave:Phase-field models
Global attractor
Omega-limit sets
Asymptotic behaviour
Descripción
Sumario:In this paper, the existence of weak solutions is established for a phase-field model of thermal alloys supplemented with Dirichlet boundary conditions. After that, the existence of global attractors for the associated multi-valued dynamical systems is proved, and the relationship among these sets is established. Finally, we provide a more detailed description of the asymptotic behaviour of solutions via the omega-limit sets. Namely, we obtain a characterization–through the natural stationary system associated to the model–of the elements belonging to the omega-limit sets under suitable assumptions.