General stability result for viscoelastic wave equations

被引:93
作者
Mustafa, Muhammad I. [1 ]
Messaoudi, Salim A. [1 ]
机构
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia
关键词
ASYMPTOTIC STABILITY; VOLTERRA EQUATION; ENERGY; DECAY; EXISTENCE; BEHAVIOR; SYSTEMS; MEMORY;
D O I
10.1063/1.4711830
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper, we consider a viscoelastic equation and establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity. Our result allows a wider class of relaxation functions and improves earlier results in the literature. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4711830]
引用
收藏
页数:14
相关论文
共 24 条
[1]   A general method for proving sharp energy decay rates for memory-dissipative evolution equations [J].
Alabau-Boussouira, Fatiha ;
Cannarsa, Piermarco .
COMPTES RENDUS MATHEMATIQUE, 2009, 347 (15-16) :867-872
[2]  
[Anonymous], 2002, J. Differ. Equ
[3]  
Arnold V. I., 2013, Mathematical methods of classical mechanics, V60
[4]   Existence and decay of solutions of a viscoelastic equation with a nonlinear source [J].
Berrimi, S ;
Messaoudi, SA .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (10) :2314-2331
[5]  
Berrimi S., 2004, Electron. J. Differ. Equations, V2004, P1
[6]  
Cabanillas E.L., 1996, Comm. Math. Phys, V177, P583, DOI DOI 10.1007/BF02099539
[7]   General decay rate estimates for viscoelastic dissipative systems [J].
Cavalcanti, M. M. ;
Cavalcanti, V. N. Domingos ;
Martinez, P. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (01) :177-193
[8]   Frictional versus viscoelastic damping in a semilinear wave equation [J].
Cavalcanti, MM ;
Oquendo, HP .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 42 (04) :1310-1324
[9]  
DAFERMOS CM, 1970, ARCH RATION MECH AN, V37, P297
[10]   AN ABSTRACT VOLTERRA EQUATION WITH APPLICATIONS TO LINEAR VISCOELASTICITY [J].
DAFERMOS, CM .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1970, 7 (03) :554-&