Robustness of time-dependent attractors in H1-norm for nonlocal problems

Tomás Caraballo; Marta Herrera-Cobos; Pedro Marín-Rubio

doi:10.3934/dcdsb.2018140

Article Contents

2018, Volume 23, Issue 3: 1011-1036. Doi: 10.3934/dcdsb.2018140

This issue Previous Article Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay Next Article Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions

Robustness of time-dependent attractors in H¹-norm for nonlocal problems

Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, c/Tarfia s/n, 41012 Sevilla, Spain

Received: February 28, 2017

Revised: April 30, 2017

Early access: February 2018

Published: June 2018

Partially funded by the projects MTM2015-63723-P (MINECO/FEDER, EU) and P12-FQM-1492 (Junta de Andalucía)

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Abstract

In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H¹-norm are analysed for a parameterized family of non-autonomous nonlocal reaction-diffusion equations without uniqueness, improving previous results [Nonlinear Dyn. 84 (2016), 35-50].

Keywords:

Non-autonomous nonlocal reaction-diffusion equations,
pullback attractors,
regularity of attractors,
upper semicontinuous behaviour.

Mathematics Subject Classification: Primary: 35B41, 35B65, 35K57, 35Q92, 37L30.

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