Nonlinear Transmission Problem for Wave Equation with Boundary Condition of Memory Type

被引：28
作者：
Bae, Jeong Ja [1 ]
机构：
[1] Dong Eui Univ, Dept Math, Pusan 614714, South Korea
来源：
ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期
关键词：
Transmission problem; Uniform decay; Wave equation; Boundary value problem; UNIFORM DECAY; KIRCHHOFF TYPE; EXISTENCE; THERMOELASTICITY; STABILITY; TERM;
D O I：
10.1007/s10440-009-9485-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider a transmission problem with a boundary damping condition of memory type, that is, the wave propagation over bodies consisting of two physically different types of materials. One component is clamped, while the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. We will study the global existence of solutions for the transmission problem, and moreover we show that if the relaxation function decays exponentially or polynomially, then the solutions for the problem have the same decay rates.
引用
收藏
页码：907 / 919
页数：13
相关论文
共 11 条
[1]  
ANDRADE D, 2006, ELECTRON J DIFFER EQ, V53, P1
[2]   On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary [J].
Bae, JJ .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (03) :351-372
[3]   Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary [J].
Cavalcanti, MM ;
Cavalcanti, VND ;
Santos, ML .
APPLIED MATHEMATICS AND COMPUTATION, 2004, 150 (02) :439-465
[4]   Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term [J].
Cavalcanti, MM ;
Cavalcanti, VND ;
Prates, JS ;
Soriano, JA .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 38 (03) :281-294
[5]   Positive solutions for a nonlinear nonlocal elliptic transmission problem [J].
Ma, TF ;
Rivera, JEM .
APPLIED MATHEMATICS LETTERS, 2003, 16 (02) :243-248
[6]   Transmission problem in thermoelasticity with symmetry [J].
Marzocchi, A ;
Rivera, JEM ;
Naso, MG .
IMA JOURNAL OF APPLIED MATHEMATICS, 2003, 68 (01) :23-46
[7]   Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity [J].
Marzocchi, A ;
Rivera, JEM ;
Naso, MG .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2002, 25 (11) :955-980
[8]   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
[9]  
Rivera JEM, 2000, ACTA APPL MATH, V62, P1
[10]   Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary [J].
Santos, ML ;
Ferreira, J ;
Pereira, DC ;
Raposo, CA .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (05) :959-976
12