摘要
研究一类非线性拟抛物方程的柯西问题.首先利用与原方程等价的积分方程以及压缩映像原理得到了问题的局部W^(k,p)解的存在性,而后在某些假设下得到了问题W^(k,p)解的整体存在性,最后利用凸性方法得到了解的有限时间内爆破.
This paper studies the Cauchy problem for a class of nonlinear pseudoparabolic equation, firstly, the existence of local Wk,p solutions is obtained by using an equivalent integral equation and the contraction mapping principle. Then under some assumptions we obtain the global existence of Wk,p solution. Finally, the blows-up in finite time of the solution is proved by the concave method.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第9期196-205,共10页
Mathematics in Practice and Theory
基金
国家自然科学基金(10926149)
黑龙江省自然科学基金(A200702
A200810)
关键词
非线性拟抛物方程
柯西问题
整体存在性
爆破
nonlinear pseudoparabolic equation
cauchy problem
global existence
blow-up
