Initial value problem for a class of fourth-order nonlinear wave equations

被引：6

作者：

Chen, Guo-wang ^{[1
]}

Hou, Chang-shun ^{[1
,2
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

[2] Henan Univ Technol, Coll Math & Phys, Zhengzhou 450052, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2009年 / 30卷 / 03期

基金：

中国国家自然科学基金;

关键词：

fourth-order nonlinear wave equation; initial value problem; global solution; blow up of solution; GENERALIZED BOUSSINESQ EQUATION; BLOW-UP; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; EXISTENCE; NONEXISTENCE;

D O I：

10.1007/s10483-009-0313-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

引用

页码：391 / 401

页数：11

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