On the standing wave in coupled non-linear Klein-Gordon equations

被引：54

作者：

Zhang, J ^{[1
]}

机构：

[1] Sichuan Normal Univ, Dept Math, Chengdu 610068, Peoples R China

[2] Univ Tokyo, Dept Math Sci, Meguro Ku, Tokyo 153, Japan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2003年 / 26卷 / 01期

关键词：

D O I：

10.1002/mma.340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the standing wave in coupled non-linear Klein-Gordon equations. By an intricate variational argument we establish the existence of standing wave with the ground state. Then we derive out the sharp criterion for blowing up and global existence by applying the potential well argument and the concavity method. We also show the instability of the standing wave. Copyright (C) 2003 John Wiley Sons, Ltd.

引用

页码：11 / 25

页数：15

共 30 条

[1]

[Anonymous], 1991, J FLUID MECH

[2] STABILITY OF SOLITARY WAVES [J].

BENJAMIN, TB .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 328 (1573) :153-+

[3]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[4]

BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489

[5] UNIQUENESS OF THE GROUND-STATE SOLUTIONS OF DELTA-U+F(U)=0 IN RN,N-GREATER-THAN-OR-EQUAL TO 3 [J].

CHEN, CC ;

LIN, CS .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (8-9) :1549-1572

[6]

COFFMAN CV, 1972, ARCH RATION MECH AN, V46, P81

[7] Ground states and free boundary value problems for the n-Laplacian in n dimensional space [J].

García-Huidobro, M ;

Manásevich, R ;

Serrin, J ;

Tang, MX ;

Yarur, CS .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 172 (01) :177-201

[8] GLOBAL SOLUTION OF THE SYSTEM OF WAVE AND KLEIN-GORDON EQUATIONS [J].

GEORGIEV, V .

MATHEMATISCHE ZEITSCHRIFT, 1990, 203 (04) :683-698

[9]

GROZDENA T, 1999, COMPTES RENDUS SEA 1, V328, P117

[10]

GROZDENA T, 1999, J MATH ANAL APPL, V239, P213

← 1 2 3 →