| 一类GBBM方程的柯西问题 |
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| 引用本文： | 于涛,莫海平,孙明丽,刘洋.一类GBBM方程的柯西问题[J].数学的实践与认识,2010,40(9). |
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| 作者姓名： | 于涛 莫海平 孙明丽 刘洋 |
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| 基金项目： | 国家自然科学基金，黑龙江省自然科学基金 |
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| 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.
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| 关 键 词： | 非线性拟抛物方程 柯西问题 整体存在性 爆破 |
Cauchy Problem for a Class of GBBM Equations |
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| YU Tao,MO Hai-ping,SUN Ming-li,LIU Yang.Cauchy Problem for a Class of GBBM Equations[J].Mathematics in Practice and Theory,2010,40(9). |
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| Authors: | YU Tao MO Hai-ping SUN Ming-li LIU Yang |
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| Abstract: | This paper studies the Cauchy problem for a class of nonlinear pseudoparabolic equation.firstly,the existence of local W~(k,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 W~(k,p) solution.Finally,the blows-up in finite time of the solution is proved by the concave method. |
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| Keywords: | nonlinear pseudoparabolic equation cauchy problem global existence blow-up |
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