Second Darboux problem for the wave equation with a power-law nonlinearity

被引：5

作者：

Kharibegashvili, S. S. ^{[1
]}

Dzhokhadze, O. M.

机构：

[1] Georgia Tech Univ, Tbilisi, Georgia

来源：

DIFFERENTIAL EQUATIONS | 2013年 / 49卷 / 12期

关键词：

CAUCHY-GOURSAT PROBLEM;

D O I：

10.1134/S0012266113120124

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the one-dimensional wave equation with a power-law nonlinearity, we consider the second Darboux problem and study the existence and uniqueness of a global solution, the existence of local solutions, and the absence of global solutions.

引用

页码：1577 / 1595

页数：19

共 21 条

[11] The first Darboux problem for wave equations with a nonlinear positive source term [J].

Jokhadze, O. ;

Midodashvili, B. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (09) :3005-3015

[12] On existence and nonexistence of global solutions of Cauchy-Goursat problem for nonlinear wave equations [J].

Jokhadze, O. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 340 (02) :1033-1045

[13] Cauchy-Goursat Problem for One-Dimensional Semilinear Wave Equations [J].

Jokhadze, O. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (04) :367-382

[14]

Kharibegashvili S, 2009, MEM DIFFER EQU MATH, V46, P1

[15]

Kharibegashvili S., 1995, Mem. Differential Equations Math. Phys., V4, P1

[16]

Ladyzhenskaya O. A., 1973, Kraevye zadachi matematicheskoi fiziki

[17]

Mitidieri E., 2001, Tr Mat Inst Steklova, V234, P1

[18]

Moiseev E.I., 1984, DIFF URAVN, V20, P73

[19]

Moiseev E.I., 1988, Uravneniya smeshannogo tipa so spektralnym parametrom (Mixed Type Equationswith Spectral Parameter)

[20]

Samarskii A.A., 1987, Blow-up Regimes in the Problems for Quasilinear Parabolic equations

← 1 2 3 →