Asymptotic behaviors of solutions for time dependent damped wave equations

被引：27

作者：

Nishihara, Kenji ^{[1
]}

Zhai, Jian ^{[2
]}

机构：

[1] Waseda Univ, Fac Polit Sci & Econ, Tokyo 1698050, Japan

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 360卷 / 02期

基金：

中国国家自然科学基金; 日本学术振兴会;

关键词：

Time dependent damped wave equation; Absorbed semilinear term; Asymptotic behavior; BLOW-UP RESULT; CAUCHY-PROBLEM; GLOBAL ASYMPTOTICS; HEAT-EQUATION; ABSORPTION; DISSIPATION; SPACE;

D O I：

10.1016/j.jmaa.2009.06.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

in this paper, we consider the Cauchy problem for the wave equation with time dependent damping b(t)u(t) and absorbed semilinear term vertical bar u vertical bar(rho-1)u. Here, b(t) = b(0)(1+ t)(-beta) with -1 < beta < 1 and b(0) > 0. Using the weighted energy method, we obtain the L(1) and L(2) decay rates of the solution. which coincide to those for self-similar solutions to the corresponding parabolic equation when 1 < rho < rho(F)(N): = 1 + 2/N @ 2009 Elsevier Inc. All rights reserved.

引用

页码：412 / 421

页数：10

共 28 条

[1]

BREZIS H, 1986, ARCH RATION MECH AN, V95, P185, DOI 10.1007/BF00251357

[2] VARIATIONAL-PROBLEMS RELATED TO SELF-SIMILAR SOLUTIONS OF THE HEAT-EQUATION [J].

ESCOBEDO, M ;

KAVIAN, O .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (10) :1103-1133

[3] NONUNIQUENESS FOR A SEMI-LINEAR INITIAL-VALUE PROBLEM [J].

HARAUX, A ;

WEISSLER, FB .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1982, 31 (02) :167-189

[4] Damped wave equation with a critical nonlinearity [J].

Hayashi, N ;

Kaikina, EI ;

Naumkin, PI .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) :1165-1185

[5] Damped wave equation in the subcritical case [J].

Hayashi, N ;

Kaikina, EI ;

Naumkin, PI .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 207 (01) :161-194

[6] On the critical nonlinear damped wave equation with large initial data [J].

Hayashi, Nakao ;

Kaikina, Elena I. ;

Naumkin, Pavel I. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (02) :1400-1425

[7]

Hayashi N, 2004, DIFFER INTEGRAL EQU, V17, P637

[8]

Ikehata R., CRITICAL EXPONENT SE

[9] Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption [J].

Ikehata, Ryo ;

Nishihara, Kenji ;

Zhao, Huijiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 226 (01) :1-29

[10] Selfsimilar profiles in large time asymptotics of solutions to damped wave equations [J].

Karch, G .

STUDIA MATHEMATICA, 2000, 143 (02) :175-197

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