PULLBACK ATTRACTOR FOR A WEAKLY DAMPED WAVE EQUATION WITH SUP-CUBIC NONLINEARITY

被引：2
作者：
Mei, Xinyu [1 ,2 ]
Xiong, Yangmin [3 ]
Sun, Chunyou [3 ]
机构：
[1] Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Guangdong, Peoples R China
[2] Shenzhen Univ, Coll Phys & Optoelect Engn, Shenzhen 518060, Guangdong, Peoples R China
[3] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 02期
关键词：
Wave equation; Locally uniform spaces; Shatah-Struwe solution; Pullback attractor; REACTION-DIFFUSION EQUATIONS; ENERGY CRITICAL WAVES; ASYMPTOTIC-BEHAVIOR; HYPERBOLIC EQUATION; PARABOLIC EQUATIONS; GLOBAL ATTRACTORS; UNBOUNDED-DOMAINS; EXISTENCE;
D O I：
10.3934/dcds.2020270
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the non-autonomous dynamical behavior of weakly damped wave equation with a sup-cubic nonlinearity is considered in locally uniform spaces. We first prove the global well-posedness of the Shatah-Struwe solutions, then establish the existence of the (H-lu(1)(R-3) x L-lu(2)(R-3), H-rho(1)(R-3) x L-rho(2)(R-3))-pullback attractor for the Shatah-Struwe solutions process of this equation. The results are based on the recent extension of Strichartz estimates for the bounded domains.
引用
收藏
页码：569 / 600
页数：32
相关论文
共 44 条
[1]   A DAMPED HYPERBOLIC EQUATION WITH CRITICAL EXPONENT [J].
ARRIETA, J ;
CARVALHO, AN ;
HALE, JK .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (5-6) :841-866
[2]   Dissipative parabolic equations in locally uniform spaces [J].
Arrieta, J. M. ;
Cholewa, J. W. ;
Dlotko, Tornasz ;
Rodriguez-Bernal, A. .
MATHEMATISCHE NACHRICHTEN, 2007, 280 (15) :1643-1663
[3]   Linear parabolic equations in locally uniform spaces [J].
Arrieta, JM ;
Rodriguez-Bernal, A ;
Cholewa, JW ;
Dlotko, T .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (02) :253-293
[4]  
Babin A.V., 1992, STUD MATH APPL, V25
[5]  
Ball JM, 2004, DISCRETE CONT DYN-A, V10, P31
[6]   Random attractors for stochastic reaction-diffusion equations on unbounded domains [J].
Bates, Peter W. ;
Lu, Kening ;
Wang, Bixiang .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (02) :845-869
[7]   Strichartz estimates for the wave equation on manifolds with boundary [J].
Blair, Matthew D. ;
Smith, Hart F. ;
Sogge, Christopher D. .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (05) :1817-1829
[8]   Global existence for energy critical waves in 3-D domains [J].
Burq, Nicolas ;
Lebeau, Gilles ;
Planchon, Fabrice .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 21 (03) :831-845
[9]  
Burq N, 2009, AM J MATH, V131, P1715
[10]   Pullback attractors for asymptotically compact non-autonomous dynamical systems [J].
Caraballo, T ;
Lukaszewicz, G ;
Real, J .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (03) :484-498
12345