Existence of solution for the n-dimension second order semilinear hyperbolic equations

被引：3

作者：

Kangqun, Zhang ^{[1
,2
]}

机构：

[1] Nanjing Inst Technol, Dept Basic Course, Nanjing 211167, Peoples R China

[2] Nanjing Univ, Dept Math & IMS, Nanjing 210093, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 381卷 / 01期

关键词：

Hyperbolic equation; Singular coefficient; Weighted estimate; Existence; CAUCHY-PROBLEM; GLOBAL EXISTENCE; REGULARITY-LOSS; COEFFICIENTS;

D O I：

10.1016/j.jmaa.2011.03.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper we establish the local and global existence of solution for the n-dimensional second order semilinear hyperbolic equation with a strongly singular coefficient which appears in the boundary-value problems of fluid dynamics. Based on the analysis about the loss of regularity on the line t = 0 for the solution of the corresponding linear equation and the decay at infinity which caused by the singular coefficient, we obtain the existence of a small solution for the semilinear equation by use of fixed point theorem. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：427 / 440

页数：14

共 15 条

[1]

[Anonymous], 1953, HIGH TRANSCEND UNPUB

[2] Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem [J].