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

共 33 条

[1] [Anonymous], 1986, Annali di Matematica Pura ed Applicata, DOI [DOI 10.1007/BF01762360.MR916688, DOI 10.1007/BF01762360]
[2] [Anonymous], 2012, Infinite-dimensional dynamical systems in mechanics and physics, DOI 10.1007/978-1-4684-0313-8
[3] Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
Ball, JM
[J]. JOURNAL OF NONLINEAR SCIENCE, 1997, 7 (05) : 475 - 502
[4] Ball JM, 2004, DISCRETE CONT DYN-A, V10, P31
[5] DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES
Carvalho, A. N.
Cholewa, J. W.
Dlotko, Tomasz
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (04) : 1147 - 1165
[6] Attractors for strongly damped wave equations with critical nonlinearities
Carvalho, AN
Cholewa, JW
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2002, 207 (02) : 287 - 310
[7] Evolution equations and their trajectory attractors
Chepyzhov, VV
Vishik, MI
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (10): : 913 - 964
[8] Chepyzhov VV., 2002, Attractors for Equations of Mathematical Physics
[9] Chueshov I., 2008, MEMORIES OF AMS, V195, pviii+183
[10] Dynamics of second order in time evolution equations with state-dependent delay
Chueshov, Igor
Rezounenko, Alexander
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 123-124 : 126 - 149

← 1 2 3 4 →