Article
Robustness of nonautonomous attractors for a family of nonlocal reaction–diffusion equations without uniqueness
Author/s | Caraballo Garrido, Tomás
![]() ![]() ![]() ![]() ![]() ![]() ![]() Herrera Cobos, Marta Marín Rubio, Pedro ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2015-06-17 |
Deposit Date | 2016-03-16 |
Published in |
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Abstract | In this paper, we consider a non-autonomous nonlocal reactiondiffusion
equation with a small perturbation in the nonlocal diffusion term
and the non-autonomous force. Under the assumptions imposed on the viscosity function, ... In this paper, we consider a non-autonomous nonlocal reactiondiffusion equation with a small perturbation in the nonlocal diffusion term and the non-autonomous force. Under the assumptions imposed on the viscosity function, the uniqueness of weak solutions cannot be guaranteed. In this multi-valued framework, the existence of weak solutions and minimal pullback attractors in the L2-norm are analysed. In addition, some relationships between the attractors of the universe of fixed bounded sets and those associated to a universe given by a tempered condition are established. Finally, the upper semicontinuity property of pullback attractors w.r.t. the parameter is proved. Indeed, under suitable assumptions, we prove that the family of pullback attractors converges to the corresponding global compact attractor associated to the autonomous nonlocal limit problem when the parameter goes to zero. |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2011-22411
![]() P12-FQM-1492 ![]() BES-2012-053398 ![]() |
Citation | Caraballo Garrido, T., Herrera Cobos, M. y Marín Rubio, P. (2015). Robustness of nonautonomous attractors for a family of nonlocal reaction–diffusion equations without uniqueness. Nonlinear Dynamics, 84 (1), 35-50. |
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