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

被引：20

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

共 35 条

[1]

Andami Ovono A., 2010, Electron. J. Diff. Equ, V134, P1

[2]

[Anonymous], 2012, Infinite-dimensional dynamical systems in mechanics and physics, DOI 10.1007/978-1-4684-0313-8

[3]

Caraballo T., P ROY SOC A IN PRESS

[4] Robustness of nonautonomous attractors for a family of nonlocal reaction-diffusion equations without uniqueness [J].

Caraballo, Tomas ;

Herrera-Cobos, Marta ;

Marin-Rubio, Pedro .

NONLINEAR DYNAMICS, 2016, 84 (01) :35-50

[5] Long-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear terms [J].

Caraballo, Tomas ;

Herrera-Cobos, Marta ;

Marin-Rubio, Pedro .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 :3-18

[6] Variable exponent, linear growth functionals in image restoration [J].

Chen, Yunmei ;

Levine, Stacey ;

Rao, Murali .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) :1383-1406

[7]

Chipot M, 2003, NONLINEAR ANALYSIS AND APPLICATIONS : TO V. LAKSHMIKANTHAM ON HIS 80TH BIRTHDAY, VOLS.1 AND 2, P431

[8]

Chipot M, 2003, REND SEMIN MAT U PAD, V110, P199

[9]

CHIPOT M, 1992, RAIRO-MATH MODEL NUM, V26, P447

[10] On the asymptotic behaviour of some nonlocal problems [J].

Chipot, M ;

Lovat, B .

POSITIVITY, 1999, 3 (01) :65-81

← 1 2 3 4 →