GLOBAL ATTRACTOR FOR A STRONGLY DAMPED WAVE EQUATION WITH FULLY SUPERCRITICAL NONLINEARITIES

被引：7

作者：

Yang, Zhijian ^{[1
]}

Liu, Zhiming ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, 100 Sci Rd, Zhengzhou 450001, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 04期

关键词：

Strongly damped wave equation; subclass of limit solutions; generalized semiflow; supercritical nonlinearities; global attractor; UNIFIED PROCEDURE; DEFORMABLE MEDIA; EVOLUTION-EQUATIONS; CONSTRUCTION; DYNAMICS;

D O I：

10.3934/dcds.2017094

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper investigates the existence of global attractor for a strongly damped wave equation with fully supercritical nonlinearities: u(tt) - Delta u - Delta u(t) + h(u(t)) + g(u) = f (x). In the case when the nonlinearities h(u(t)) and g(u) are of fully supercritical growth, which leads to that the weak solutions of the equation lose their uniqueness, by introducing the notion of limit solutions and using the theory on the attractor of the generalized semiflow, we establish the existence of global attractor for the subclass of limit solutions of the equation in natural energy space in the sense of strong topology.

引用

页码：2181 / 2205

页数：25

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