Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
In this paper, we prove some regularity results for pullback attractors of a non-autonomous reaction–diffusion model with dynamical boundary conditions considered in Anguiano (2011). Under certain assumptions of the nonlinear terms we show a regularity result for the unique solution of the problem....
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/25952 |
| Acceso en línea: | http://hdl.handle.net/11441/25952 https://doi.org/10.1016/j.nonrwa.2014.05.003 |
| Access Level: | acceso abierto |
| Palabra clave: | Reaction–diffusion equations Dynamical boundary conditions Pullback attractors Tempered exponential growth |
| Sumario: | In this paper, we prove some regularity results for pullback attractors of a non-autonomous reaction–diffusion model with dynamical boundary conditions considered in Anguiano (2011). Under certain assumptions of the nonlinear terms we show a regularity result for the unique solution of the problem. We establish a general result about boundedness of invariant sets for the associated evolution process in the norm of the domain of the spatial linear operator appearing in the equation. As a consequence, we deduce that the pullback attractors of the model are bounded in this domain norm. After that, under additional assumptions, some exponential growth results for pullback attractors when time goes to −∞ are proved. |
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