Article
Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
Author/s | Caraballo Garrido, Tomás
Herrera Cobos, Marta Marín Rubio, Pedro |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2018-03 |
Deposit Date | 2017-12-11 |
Published in |
|
Abstract | In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion ... In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion type. Firstly, we prove the existence of weak solutions making use of a change of variable which allows us to get rid of the nonlocal operator in the diffusion term. Thereupon, the regularising effect of the equation is shown applying an argument of a posteriori regularity, since under the assumptions made we cannot guarantee the uniqueness of weak solutions. In addition, this argument allows to ensure the existence of an absorbing family in W1,p 0 (Ω). This leads to the existence of the minimal pullback attractors in L2(Ω), Lp(Ω) and some other spaces as Lp∗−(Ω). Relationships between these families are also established. |
Project ID. | MTM2015-63723-P
P12-FQM-1492 BES-2012-053398 |
Citation | Caraballo Garrido, T., Herrera Cobos, M. y Marín Rubio, P. (2018). Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems. Journal of Mathematical Analysis and Applications, 459 (2), 997-1015. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Asymptotic behaviour of nonlocal ... | 344.3Kb | [PDF] | View/ | |