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Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions

 

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Opened Access Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
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Author: Anguiano Moreno, María
Marín Rubio, Pedro
Real Anguas, José
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2014
Published in: Nonlinear Analysis: Real World Applications, 112-125
Document type: Article
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 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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Format: PDF

URI: http://hdl.handle.net/11441/25952

DOI: http://dx.doi.org/10.1016/j.nonrwa.2014.05.003

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