Existence of time-dependent attractor of wave equation in locally uniform space

被引：0

作者：

Luo, Xudong ^{[1
]}

Ma, Qiaozhen ^{[2
,3
]}

机构：

[1] Gansu Univ Polit Sci & Law, Sch Artificial Intelligence, Lanzhou, Peoples R China

[2] Northwest Normal Univ, Coll Math & Stat, Lanzhou, Peoples R China

[3] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China

来源：

MATHEMATICS AND MECHANICS OF SOLIDS | 2024年 / 29卷 / 05期

关键词：

Wave equation; contractive function; time-dependent attractor; locally uniform space; EVOLUTION-EQUATIONS; UNBOUNDED-DOMAINS; GLOBAL ATTRACTOR;

D O I：

10.1177/10812865231219199

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this article, we study non-autonomous dynamical behavior of weakly damped wave equation in unbounded domain. First of all, we introduce the time-dependent locally uniform space. After that, the pullback asymptotical compactness is proved by applying the contractive function method. Eventually, we obtain the existence of ( H lu 1 ( R 3 )x L lu 2 ( R 3 ), H rho 1 ( R 3 )x L rho 1 ( R 3 )) -time-dependent attractor of wave equation.

引用

页码：944 / 958

页数：15

共 19 条

[1] EXISTENCE AND FINITE DIMENSIONALITY OF THE GLOBAL ATTRACTOR FOR EVOLUTION-EQUATIONS ON UNBOUNDED-DOMAINS [J].

ABERGEL, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) :85-108

[2]

[Anonymous], 1969, Quelques mthodes de rsolution des problmes aux limites non linaires

[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] ATTRACTORS OF PARTIAL-DIFFERENTIAL EVOLUTION-EQUATIONS IN AN UNBOUNDED DOMAIN [J].

BABIN, AV ;

VISHIK, MI .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 116 :221-243

[5] Attractors for processes on time-dependent spaces. Applications to wave equations [J].

Conti, Monica ;

Pata, Vittorino ;

Temam, Roger .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (06) :1254-1277

[6]

Di Plinio F., 2012, Bollettino dellUnione Matematica Italiana, V5, P19

[7] TIME-DEPENDENT ATTRACTOR FOR THE OSCILLON EQUATION [J].

Di Plinio, Francesco ;

Duane, Gregory S. ;

Temam, Roger .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (01) :141-167

[8]

Feireisl E., 1996, Differ. Inte- gral Equ., V9, P1147

[9] Time-dependent attractor for plate equations on Rn [J].

Liu, Tingting ;

Ma, Qiaozhen .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) :315-332

[10] PULLBACK ATTRACTOR FOR A WEAKLY DAMPED WAVE EQUATION WITH SUP-CUBIC NONLINEARITY [J].

Mei, Xinyu ;

Xiong, Yangmin ;

Sun, Chunyou .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (02) :569-600

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