General decay of solutions of a wave equation with a boundary control of memory type

被引：45

作者：

Messaoudi, Salim A. ^{[1
]}

Soufyane, Abdelaziz ^{[2
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Coll Engn & Appl Sci, Abu Dhabi, U Arab Emirates

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 04期

关键词：

General decay; Memory type; Boundary damping; Wave; Relaxation function; UNIFORM DECAY; KIRCHHOFF TYPE; STABILIZATION; EXISTENCE; RATES; FEEDBACK; SYSTEMS; TERM;

D O I：

10.1016/j.nonrwa.2009.10.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a semilinear wave equation, in a bounded domain, where the memory-type damping is acting on a part of the boundary. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. Our work allows certain relaxation functions which are not necessarily of exponential or polynomial decay and, therefore, generalizes and improves earlier results in the literature. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2896 / 2904

页数：9

共 24 条

[11]

KOMORNIK V, 1993, CHINESE ANN MATH B, V14, P153

[12]

KOMORNIK V, 1990, J MATH PURE APPL, V69, P33

[13]

Komornik V, 1997, ASYMPTOTIC ANAL, V14, P339

[14] STABILIZATION OF WAVE AND PLATE-LIKE EQUATIONS WITH NONLINEAR DISSIPATION ON THE BOUNDARY [J].

LASIECKA, I .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 79 (02) :340-381

[15] Boundary stabilization of solutions of a nonlinear system of Timoshenko type [J].

Messaoudi, Salim A. ;

Soufyane, Abdelaziz .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (07) :2107-2121

[16] On the control of solutions of viscoelastic equations with boundary feedback [J].

Messaoudi, Salim A. ;

Mustafa, Muhammad Islam .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (05) :3132-3140

[17] Uniform decay of solution for wave equation of Kirchhoff type with nonlinear boundary damping and memory term [J].

Park, JY ;

Bae, JJ ;

Jung, IH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 50 (07) :871-884

[18]

Rivera JEM, 2000, MATH METHOD APPL SCI, V23, P41, DOI 10.1002/(SICI)1099-1476(20000110)23:1<41::AID-MMA102>3.0.CO

[19]

2-B

[20] A boundary condition with memory for Kirchhoff plates equations [J].

Santos, MD ;

Junior, F .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 148 (02) :475-496

← 1 2 3 →