TIME-DEPENDENT ASYMPTOTIC BEHAVIOR OF THE WAVE EQUATION WITH STRONG DAMPING ON RN

被引：0
作者：
Luo, Xudong [1 ]
Ma, Qiaozhen [1 ]
机构：
[1] Northwest Normal Univ, Coll Math & Stat, Anningdong Rd, Lanzhou 730070, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2023年 / 13卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Wave equation; critical exponent; well-posedness; time-dependent attractor; pullback exponential attractor; UNIFIED PROCEDURE; DEFORMABLE MEDIA; ATTRACTORS; CONSTRUCTION; DYNAMICS; MODELS;
D O I：
10.11948/20220264
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the longtime dynamics of non-autonomous wave equations with strong damping in the case of critical nonlinearity. First of all, when 1 <= p <= p(*)=N+2/(N-2)+, we get the well-posedness of strong damped equation with dime-dependent decay coefficient in H-t=H-1(R-N)xL(2)(R-N), and prove the quasi-stability of weak solution in H-t,H--1=H-1(R-N)xH(-1)(R-N). Then the time-dependent attractor is proved in Ht. Finally, by using the quasi-stability of weak solution, we establish the existence the pullback exponential attractor for non-autonomous dynamical system (U(t,tau),H-t,H-t,H--1).
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页码：2387 / 2407
页数：21
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