| 高阶广义微扰KdV方程整体解的存在性 |
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| 引用本文： | 王艳红.高阶广义微扰KdV方程整体解的存在性[J].安徽大学学报(自然科学版),2010,34(2). |
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| 作者姓名： | 王艳红 |
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| 作者单位： | 河南理工大学,数学系,河南,焦作,454000 |
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| 基金项目： | 河南省高校科技创新人才支持计划资助项目，河南理工大学青年基金重点资助项目 |
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| 摘 要： | 考虑高阶广义微扰的KdV方程,讨论当参数,δε恒等于1时其初值问题整体解的存在性.借助于半群理论,引入算子A,利用Sobolev空间的基本理论和能量积分的方法,证明了当初值u0和流函数f分别满足一定的条件时,其存在唯一的整体古典解.
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| 关 键 词： | 高阶广义微扰KdV方程 整体解 能量积分方法 |
Existence of global solution for generalized KdV equation with high order perturbation terms |
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| WANG Yan-hong.Existence of global solution for generalized KdV equation with high order perturbation terms[J].Journal of Anhui University(Natural Sciences),2010,34(2). |
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| Authors: | WANG Yan-hong |
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| Abstract: | We considered the generalized KdV equation with high order perturbation terms, and discussed the global existence of the solution to the initial value problem when δ≡1,ε≡1. With semigroup theory we introduced operator A. By using the basic theory of Sobolev space and energy integral method, we proved that when the initial value u_0 and the flow function f satisfied certain conditions, there existed a unique global classic solution. |
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| Keywords: | generalized KdV equation with high order perturbation terms global solution energy integral method |
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