Existence and Characterization of Attractors for a Nonlocal Reaction-Diffusion Equation with an Energy Functional

被引：8

作者：

Caballero, R. ^{[1
]}

Marin-Rubio, P. ^{[2
]}

Valero, Jose ^{[1
]}

机构：

[1] Univ Miguel Hernandez de Elche, Ctr Invest Operat, Avda Univ S-N, Alicante 03202, Spain

[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Seville 41012, Spain

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2022年 / 34卷 / 01期

关键词：

Reaction– diffusion equations; Nonlocal equations; Global attractors; Multivalued dynamical systems; Structure of the attractor;

D O I：

10.1007/s10884-020-09933-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. Firstly, we prove the existence and uniqueness of regular and strong solutions. Secondly, we obtain the existence of global attractors in both situations under rather weak assumptions by defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Thirdly, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories.

引用

页码：443 / 480

页数：38

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