MINIMALITY PROPERTIES OF SET-VALUED PROCESSES AND THEIR PULLBACK ATTRACTORS

被引：29

作者：

Zelati, Michele Coti ^{[1
]}

Kalita, Piotr ^{[2
]}

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2015年 / 47卷 / 02期

基金：

美国国家科学基金会;

关键词：

nonautonomous parabolic problems; multivalued processes; asymptotic behavior; pullback attractors; infinite-dimensional dynamical systems; PARABOLIC HEMIVARIATIONAL INEQUALITIES; UNIFORM GLOBAL ATTRACTORS; MULTIVALUED SEMIFLOWS; DYNAMICAL-SYSTEMS; EXISTENCE; EQUATIONS; APPROXIMATION; SEMIGROUPS; REGULARITY;

D O I：

10.1137/140978995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties with respect to the notion of pullback attraction. When invariance is required, a very weak closed graph condition on the solving operators is assumed. The presentation is complemented with examples and counterexamples to test the sharpness of the hypotheses involved, including a reaction-diffusion equation, a discontinuous ordinary differential equation, and an irregular form of the heat equation.

引用

页码：1530 / 1561

页数：32

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