Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms

被引：77

作者：

Messaoudi, Salim A. ^{[2
]}

Said-Houari, Belkacem ^{[1
]}

机构：

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

[2] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期

关键词：

Blow up; Global nonexistence; Positive initial energy; Viscoelastic wave equations; BLOW-UP; CAUCHY-PROBLEM; EVOLUTION-EQUATIONS; EXISTENCE; THEOREMS;

D O I：

10.1016/j.jmaa.2009.10.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：277 / 287

页数：11

共 25 条

[1] Agre K, 2006, DIFFER INTEGRAL EQU, V19, P1235
[2] REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NON-LINEAR EVOLUTION EQUATIONS
BALL, JM
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1977, 28 (112) : 473 - 486
[3] EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS
GEORGIEV, V
TODOROVA, G
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) : 295 - 308
[4] Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source
Han, Xiaosen
Wang, Mingxin
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (11) : 5427 - 5450
[5] DECAY-ESTIMATES FOR SOME SEMILINEAR DAMPED HYPERBOLIC PROBLEMS
HARAUX, A
ZUAZUA, E
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1988, 100 (02) : 191 - 206
[6] KAFINI M, 2006, ELECT J DIFFERENTIAL, V113, P1
[7] A blow-up result in a Cauchy viscoelastic problem
Kafini, Mohammad
Messaoudi, Salim A.
[J]. APPLIED MATHEMATICS LETTERS, 2008, 21 (06) : 549 - 553
[8] Kalantarov V. K., 1978, J SOVIET MATH, V10, P53, DOI 10.1007/BF01109723
[9] INSTABILITY AND NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS OF FORM PUTT = -AU + F(U)
LEVINE, HA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 192 : 1 - 21
[10] SOME ADDITIONAL REMARKS ON NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS
LEVINE, HA
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (01) : 138 - 146

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