Periodic solutions of a quasilinear wave equation

被引：2

作者：

Kondrat'ev, V. A. ^{[1
]}

Rudakov, I. A. ^{[2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

[2] Bryansk State Univ, Bryansk, Russia

来源：

MATHEMATICAL NOTES | 2009年 / 85卷 / 1-2期

关键词：

quasilinear wave equation; sine-Gordon equation; boundary condition of the third kind; Dirichlet boundary condition; Sturm-Liouville problem; Sobolev space; HOMOGENEOUS BOUNDARY-CONDITIONS; FORCED VIBRATIONS; COEFFICIENTS;

D O I：

10.1134/S0001434609010040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the properties of wave operators satisfying the periodicity condition with respect to time and homogeneous boundary conditions of the third kind and of Dirichlet type. We prove the existence of a nontrivial periodic (in time) sine-Gordon solution with homogeneous boundary conditions of the third kind and of Dirichlet type. We obtain theorems on the existence of periodic solutions of a quasilinear wave equation with variable (in x) coefficients and a boundary condition of the third kind.

引用

页码：34 / 50

页数：17

共 50 条

[21] PERIODIC SOLUTIONS OF A NONLINEAR WAVE EQUATION
STEWART, FM
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1954, 60 (04) : 344 - 344
[22] Existence of an anti-periodic solution for the quasilinear wave equation with viscosity
Nakao, M
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 204 (03) : 754 - 764
[23] Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima
Pinto, M
Trofimchuk, S
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2000, 130 : 1103 - 1118
[24] Periodic solutions of the quasilinear beam vibration equation with homogeneous boundary conditions
Rudakov, I. A.
DIFFERENTIAL EQUATIONS, 2012, 48 (06) : 820 - 831
[25] Periodic solutions of the quasilinear beam vibration equation with homogeneous boundary conditions
I. A. Rudakov
Differential Equations, 2012, 48 : 820 - 831
[26] Global smooth solutions for the quasilinear wave equation with boundary dissipation
Yao, Peng-Fei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 241 (01) : 62 - 93
[27] Global smooth solutions for the quasilinear wave equation with boundary dissipation
Yao, Peng-Fei
2006 CHINESE CONTROL CONFERENCE, VOLS 1-5, 2006, : 2254 - 2257
[28] Asymptotic expansions of traveling wave solutions for a quasilinear parabolic equation
Koichi Anada
Tetsuya Ishiwata
Takeo Ushijima
Japan Journal of Industrial and Applied Mathematics, 2022, 39 : 889 - 920
[29] STRONG SOLUTIONS OF A QUASILINEAR WAVE-EQUATION WITH NONLINEAR DAMPING
ANG, DD
DINH, APN
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1988, 19 (02) : 337 - 347
[30] ON EXACT SOLUTIONS OF A DEGENERATE QUASILINEAR WAVE EQUATION WITH SOURCE TERM
Amroun, Nour-Eddine
Benaissa, Abbes
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,

← 1 2 3 4 5 →