Article
Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
Author/s | Anguiano Moreno, María
Marín Rubio, Pedro Real Anguas, José |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2014 |
Deposit Date | 2015-06-23 |
Published in |
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Abstract | 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 ... 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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