Parametric resonance and nonexistence of the global solution to nonlinear wave equations

被引：9

作者：

Yagdjian, K ^{[1
]}

机构：

[1] Univ Tsukuba, Inst Math, Tsukuba, Ibaraki 305, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2001年 / 260卷 / 01期

关键词：

parametric resonance; nonlinear wave equations; global solution;

D O I：

10.1006/jmaa.2000.7469

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an example of the influence of the dependence of the coefficient of equation on time variable, and in particular oscillations in time, on a global existence of the solution to the nonlinear hyperbolic equation. Namely for arbitrary small initial data we construct a blowing up solution. (C) 2001 Academic Press.

引用

页码：251 / 268

页数：18

共 19 条

[11] Magnus W., 1966, HILLS EQUATION
[12] Remarks on the blow-up boundaries and rates for nonlinear wave equations
Ohta, M
Takamura, H
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 33 (07) : 693 - 698
[13] Racke R., 1992, LECT NONLINEAR EVOLU
[14] Reissig M, 1999, MATH METHOD APPL SCI, V22, P937, DOI 10.1002/(SICI)1099-1476(19990725)22:11<937::AID-MMA28>3.0.CO
[15] 2-O
[16] REISSIG M, 1998, TU BERGAKADEMIE FREI
[17] Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms
Todorova, G
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 326 (02): : 191 - 196
[18] TODOROVA G, 2000, NONLINEAR ANAL, V41
[19] Yakubovich V. A., 1975, LINEAR DIFFERENTIAL, V1

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