EXPONENTIAL DECAY FOR SOLUTIONS TO SEMILINEAR DAMPED WAVE EQUATION

被引：30

作者：

Gerbi, Stephane ^{[1
]}

Said-Houari, Belkacem ^{[2
]}

机构：

[1] Univ Savoie, Math Lab, F-73376 Le Bourget Du Lac, France

[2] KAUST, Div Math & Comp Sci & Engn, Thuwal 239556900, Saudi Arabia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2012年 / 5卷 / 03期

关键词：

Strong damping; stable set; global existence; decay rate; positive initial energy; GLOBAL-SOLUTIONS; NONEXISTENCE THEOREMS; EVOLUTION-EQUATIONS; CAUCHY-PROBLEM; BLOW-UP; EXISTENCE; INSTABILITY;

D O I：

10.3934/dcdss.2012.5.559

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].

引用

页码：559 / 566

页数：8

共 22 条

[1] REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NON-LINEAR EVOLUTION EQUATIONS [J].

BALL, JM .

QUARTERLY JOURNAL OF MATHEMATICS, 1977, 28 (112) :473-486

[2] Exponential decay of solutions of a nonlinearly damped wave equation [J].

Benaissa, A ;

Messaoudi, S .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2006, 12 (04) :391-399

[3] Qualitative analysis of a nonlinear wave equation [J].

Esquivel-Avila, JA .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2004, 10 (03) :787-804

[4] The dynamics of a nonlinear wave equation [J].

Esquivel-Avila, JA .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 279 (01) :135-150

[5] Global solutions and finite time blow up for damped semilinear wave equations [J].

Gazzola, F ;

Squassina, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (02) :185-207

[6] EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS [J].

GEORGIEV, V ;

TODOROVA, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) :295-308

[7] DECAY-ESTIMATES FOR SOME SEMILINEAR DAMPED HYPERBOLIC PROBLEMS [J].

HARAUX, A ;

ZUAZUA, E .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1988, 100 (02) :191-206

[8] Some remarks on the wave equations with nonlinear damping and source terms [J].

Ikehata, R .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 27 (10) :1165-1175

[9]

Ikehata R., 1996, HIROSHIMA MATH J, V26, P475, DOI DOI 10.32917/HMJ/1206127254

[10]

Kalantarov V. K., 1978, J SOVIET MATH, V10, P53, DOI 10.1007/BF01109723

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