GLOBAL SOLVABILITY OF NONLINEAR-WAVE EQUATION WITH A VISCOELASTIC BOUNDARY-CONDITION

被引：0
作者：
QIN, TH
机构：
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 1993年 / 14卷 / 03期
关键词：
NONLINEAR WAVE EQUATION; VISCOELASTIC BOUNDARY CONDITION; GLOBAL SOLVABILITY;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper deals with the global solvability of nonlinear wave equation with a viscoelastic boundary condition. The problem is a mathematical mode for nonlinare one-dimensional motion of an elastic bar connected with a viscoelastic element at one end of the bar. Under some physically reasonable assumptions, the boundary condition is dissipative and the existence of global smooth solution of the problem is proved for small data.
引用
收藏
页码：335 / 346
页数：12
相关论文
共 50 条
[1]   Control of a nonlinear wave equation with a dynamic boundary condition [J].
Madureira, Rodrigo L. R. ;
Rincon, Mauro A. ;
Apolaya, Ricardo F. ;
Carmo, Bruno A. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 176 :140-149
[2]   Solvability Issues of a Pseudo-Parabolic Fractional Order Equation with a Nonlinear Boundary Condition [J].
Aitzhanov, Serik E. ;
Berdyshev, Abdumauvlen S. ;
Bekenayeva, Kymbat S. .
FRACTAL AND FRACTIONAL, 2021, 5 (04)
[3]   Exponential decay of non-linear wave equation with a viscoelastic boundary condition [J].
Rivera, JEM ;
Andrade, D .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2000, 23 (01) :41-61
[4]   RESONANCE AND NEAR-RESONANCE FOR A NONLINEAR-WAVE EQUATION [J].
BLOM, CJ ;
VAVILOV, SA .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (02) :109-143
[5]   Global solvability of initial boundary-value problems for nonlinear analogs of the Boussinesq equation [J].
Amirov, Sh. ;
Kozhanov, A. I. .
MATHEMATICAL NOTES, 2016, 99 (1-2) :183-191
[6]   Global solvability of initial boundary-value problems for nonlinear analogs of the Boussinesq equation [J].
Sh. Amirov ;
A. I. Kozhanov .
Mathematical Notes, 2016, 99 :183-191
[7]   EXISTENCE AND ASYMPTOTIC EXPANSION OF SOLUTIONS TO A NONLINEAR WAVE EQUATION WITH A MEMORY CONDITION AT THE BOUNDARY [J].
Nguyen Thanh Long ;
Le Xuan Truong .
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[8]   Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping [J].
Cícero Lopes Frota ;
André Vicente .
Zeitschrift für angewandte Mathematik und Physik, 2018, 69
[9]   Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping [J].
Frota, Cicero Lopes ;
Vicente, Andre .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (03)
[10]   Global solvability for nonlinear wave equations with singular potential [J].
Georgiev, Vladimir ;
Kubo, Hideo .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 375 :514-537
12345