GLOBAL ATTRACTOR FOR A NONLOCAL p-LAPLACIAN EQUATION WITHOUT UNIQUENESS OF SOLUTION

被引：18

作者：

Caraballo, Tomas ^{[1
]}

Herrera-Cobos, Marta ^{[1
]}

Marin-Rubio, Pedro ^{[1
]}

机构：

[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, E-41080 Seville, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2017年 / 22卷 / 05期

关键词：

Nonlocal p-Laplacian equation; compact global attractor; asymptotic compactness; multi-valued dynamical systems;

D O I：

10.3934/dcdsb.2017107

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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(Omega) is ensured.

引用

页码：1801 / 1816

页数：16

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