DYNAMICS FOR THE DAMPED WAVE EQUATIONS ON TIME-DEPENDENT DOMAINS

被引：10
作者：
Zhou, Feng [1 ,2 ]
Sun, Chunyou [2 ]
Li, Xin [3 ]
机构：
[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
[3] Yanshan Univ, Coll Sci, Qinhuangdao 066004, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 04期
关键词：
Non-autonomous dynamical systems; wave equation; time-dependent domain; critical exponent; pullback attractor; REACTION-DIFFUSION EQUATIONS; SEMILINEAR HEAT-EQUATION; FREE-BOUNDARY PROBLEM; PULLBACK ATTRACTORS; GLOBAL ATTRACTORS; SCHROEDINGER-TYPE; CONTINUITY; WATER;
D O I：
10.3934/dcdsb.2018068
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the asymptotic dynamics of a damped wave equations on a time-dependent domains with homogeneous Dirichlet boundary condition, the nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. To this end, we establish the existence and uniqueness of strong and weak solutions satisfying energy inequality under the assumption that the spatial domains O-t in R-3 are obtained from a bounded base domain O by a C-3-diffeomorphism r (., t). Furthermore, we establish the pullback attractor under a slightly weaker assumption that the measure of the spatial domains are uniformly bounded above.
引用
收藏
页码：1645 / 1674
页数：30
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