ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING:GLOBAL EXISTENCE,DECAY AND BLOWUP OF THE SOLUTION

被引：0

作者：

Abderrahmane ZARA ^{[1
]}

Nasser-eddine TATAR ^{[2
]}

Salem ABDELMALEK ^{[3
,1
]}

机构：

[1] Depatment of Mathematics and Informatic,Cheikh El Arbi Tébessi University,12002 Tébessa,Algeria

[2] Depatment of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran 31261,Saudi Arabia

[3] Depatment of Mathematics,College of Sciences,Yanbu,Taibah University,Saudi Arabia

来源：

ActaMathematicaScientia | 2013年 / 33卷 / 01期

关键词：

elastic membrane equation; global existence; boundary damping; boundary source; general decay; blowup;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping.Under some appropriate assumptions on the relaxation function h and with certain initial data,the global existence of solutions and a general decay for the energy are established using the multiplier technique.Also,we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.

引用

页码：84 / 106

页数：23

共 10 条

[1] Decay estimates for second order evolution equations with memory[J] . Fatiha Alabau-Boussouira,Piermarco Cannarsa,Daniela Sforza.Journal of Functional Analysis . 2007 (5)
[2] Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping–source interaction[J] . Marcelo M. Cavalcanti,Valéria N. Domingos Cavalcanti,Irena Lasiecka.Journal of Differential Equations . 2007 (2)
[3] Existence and nonexistence of global solutions of some system of semilinear wave equations
Li, MR
Tsai, LY
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (08) : 1397 - 1415
[4] Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term
Aassila, M
Cavalcanti, MM
Cavalcanti, VND
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2002, 15 (02) : 155 - 180
[5] Global existence for the wave equation with nonlinear boundary damping and source terms
Vitillaro, E
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 186 (01) : 259 - 298
[6] Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping[J] . M. M. Cavalcanti,V. N. Domingos Cavalcanti,J. S. Prates Filho,J. A. Soriano.Differential and Integral Equations . 2001 (1)
[7] Existence and Exponential Decay for a Kirchhoff–Carrier Model with Viscosity[J] . M.M Cavalcanti,V.N Domingos Cavalcanti,J.S Prates Filho,J.A Soriano.Journal of Mathematical Analysis and Applications . 1998 (1)
[8] On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation
Ono, K
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 216 (01) : 321 - 342
[9] Global Existence, Decay, and Blowup of Solutions for Some Mildly Degenerate Nonlinear Kirchhoff Strings[J] . Kosuke Ono.Journal of Differential Equations . 1997 (2)
[10] Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain. M. Aassila,M.M. Cavalcanti,J.A. Soriano. The SIAM Journal on Control and Optimization . 2000

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