On the solvability of a boundary value problem for nonlinear wave equations in angular domains

被引：2

作者：

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

Jokhadze, O. M.

机构：

[1] Tbilisi Ivane Javakhishvili State Univ, A Razmadze Math Inst, Tbilisi, Georgia

来源：

DIFFERENTIAL EQUATIONS | 2016年 / 52卷 / 05期

关键词：

CAUCHY-GOURSAT PROBLEM;

D O I：

10.1134/S0012266116050104

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a one-dimensional wave equation with a weak nonlinearity, we study the Darboux boundary value problem in angular domains, for which we analyze the existence and uniqueness of a global solution and the existence of local solutions as well as the absence of global solutions.

引用

页码：644 / 666

页数：23

共 20 条

[1]

[Anonymous], USPEKHI MAT NAUK

[2]

[Anonymous], 2001, T MAT I STEKLOVA

[3]

Berikelashvili G.K., 2008, DIFF URAVN, V44, P359

[4]

Dzhokhadze O. M., 2008, Mat. Zametki, V84, P693

[5]

Fikhtengol'ts G.M., 1969, KURS DIFFERENTSIALNO

[6]

GILBARG D., 2015, Elliptic Partial Differential Equations of Second Order

[7]

Goman O.G., 1968, VESTN MOSKOV U MAT M, P84

[8] 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

[9] 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

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

Jokhadze, O. .

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

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