Global existence and energy decay of solutions to a nonlinear wave equation with a delay term

被引：15

作者：

Benaissa, Abbes ^{[1
]}

Louhibi, Naima ^{[1
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, Lab Anal & Control Partial Differential Equat, Sidi Bel Abbes 22000, Algeria

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2013年 / 20卷 / 01期

关键词：

Nonlinear wave equation; delay term; decay rate; multiplier method; BOUNDARY; STABILIZATION; RATES;

D O I：

10.1515/gmj-2013-0006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the nonlinear wave equation in a bounded domain with a delay term in the internal feedback u ''(x, t) - Delta(x)u(x, t) + mu(1)g(u'(x, t)) + mu(2)g(u'(x, t - tau)) = 0 and prove the global existence of its solutions in Sobolev spaces by means of the energy method combined with the Faedo-Galerkin procedure under a certain condition between the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behavior of solutions using the multiplier method and general weighted integral inequalities.

引用

页码：1 / 24

页数：24

共 27 条

[1]

ABDALLAH C, 1993, PROCEEDINGS OF THE 1993 AMERICAN CONTROL CONFERENCE, VOLS 1-3, P3106

[2] Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems [J].

Alabau-Boussouira, F .

APPLIED MATHEMATICS AND OPTIMIZATION, 2005, 51 (01) :61-105

[3]

[Anonymous], 1993, DIFFER INTEGR EQUATI

[4]

[Anonymous], ESAIM CONTROL OPTIM

[5]

Arnold V. I., 2013, Mathematical methods of classical mechanics, V60

[6]

Benaissa A, 2008, ELECTRON J DIFFER EQ

[7] Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction [J].

Cavalcanti, Marcelo M. ;

Cavalcanti, Valeria N. Domingos ;

Lasiecka, Irena .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 236 (02) :407-459

[8] CONTROL AND STABILIZATION FOR THE WAVE-EQUATION IN A BOUNDED DOMAIN, PART .2. [J].

CHEN, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1981, 19 (01) :114-122

[9] CONTROL AND STABILIZATION FOR THE WAVE-EQUATION IN A BOUNDED DOMAIN [J].

CHEN, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1979, 17 (01) :66-81

[10] UNIFORM ENERGY DECAY FOR A WAVE EQUATION WITH PARTIALLY SUPPORTED NONLINEAR BOUNDARY DISSIPATION WITHOUT GROWTH RESTRICTIONS [J].

Daoulatli, Moez ;

Lasiecka, Irena ;

Toundykov, Daniel .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2009, 2 (01) :67-94

← 1 2 3 →