Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution

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

doi:10.3934/dcdsb.2017107

Article Contents

2017, Volume 22, Issue 5: 1801-1816. Doi: 10.3934/dcdsb.2017107

This issue Previous Article Attractors for a random evolution equation with infinite memory: Theoretical results Next Article Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic

Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution

Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160,41080-Sevilla, Spain

Received: February 2016

Revised: June 2016

Published: August 2017

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 solution for a $p$ -Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal one but with local diffusion. Since the uniqueness of solution is unknown, the asymptotic behaviour of the solutions is analysed in a multi-valued framework. Namely, the existence of the compact global attractor in $L^2(Ω)$ is ensured.

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Mathematics Subject Classification: Primary:35B41, 35K55, 35Q92, 37L30.

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