摘要
该文研究一类非线性高阶波动方程u_(tt)-a_1u_(xx)+a_2u_(x^4)+a_3u_(x^4_(tt))=ф(u_x)_x+f(u,u_x,u_(xx)u_(xxx),u_(x^4))的初边值问题.证明整体古典解的存在唯一性并给出古典解爆破的充分条件.
In this paper the initial boundary value problems for a class of nonlinear wave equation utt-a1uxx＋a2ux4＋a3ux4tt）=ф（ux）x＋f（u,ux,uxxuxxx,ux4）are considered. The existence and uniqueness of the classical global solution are proved. The sufficient conditions of blow-up of solutions are given.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2007年第4期624-640,共17页
Acta Mathematica Scientia
基金
国家自然科学基金(10671182)资助
关键词
非线性高阶波动方程
初边值问题
整体古典解
解的爆破
GREEN函数
Nonlinear wave equation of higher order
Initial boundary value problem
Classical global solution
Blow-up of solution
Green function.
