[1]吴建成,沃松林.一类伪抛物方程的非线性扰动[J].南京理工大学学报(自然科学版),2006,(03):381-384.
 WU Jian-cheng~,WO Song-lin~.Nonlinear Perturbation for a Class of Pseudoparabolic Equations[J].Journal of Nanjing University of Science and Technology,2006,(03):381-384.
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一类伪抛物方程的非线性扰动
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《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
2006年03期
页码:
381-384
栏目:
出版日期:
2006-06-30

文章信息/Info

Title:
Nonlinear Perturbation for a Class of Pseudoparabolic Equations
作者:
吴建成1 沃松林2
1. 江苏工业学院信息科学系, 江苏常州213164; 2. 常州信息职业技术学院基础部, 江苏常州213164
Author(s):
WU Jian-cheng~1WO Song-lin~2
1.Department of Information Science,Jiangsu Polytechnic University,Changzhou 213164,China;2.Academic Affairs Office,Changzhou College of Information Technology,Changzhou 213164,China
关键词:
伪抛物型方程 非线性扰动 同胚 解的存在性
Keywords:
pseudoparabo lic equation non linear perturbation homeomorphism ex istence of the solution
分类号:
O 175. 29
摘要:
非线性伪抛物方程和一些重要的物理过程有着密切的关系,研究了一类伪抛物方程Δu+ut-ut-f(x,t,u)=F x,t,u,xui初边值问题的非线性扰动问题。首先在Hilbert空间中建立了强制不等式,利用同胚方法和抽象的反函数定理,得到了半线性伪抛物方程初边值问题解的存在性和惟一性定理。在此基础上,讨论了对应的非线性扰动。通过构造相应的紧算子,利用同伦对算子进行估计并利用Schauder不动点定理,给出了非线性扰动问题解的存在定理。
Abstract:
Th is paper discusses the nonlinear perturbation o f the in itia-l boundary value prob lem s for a c lass of non linear pseudoparabo lic equa tions $ u + 5u 5t - 5u 5t - f (x, t, u) = F x, t, u, 5u 5xi . A coerciv ity inequality inH ilbert space is founded. By using homeomorph ism method and the ex tended inverse function theorem, the ex istence and un iqueness o f the solution for the sem -i linear pseudoparabo lic equat ions is obta ined. Based on this, the relevant non linear perturbation of the problems is proposed. Through constructing a corresponding compact operator, estimating the operator w ith homotopic method and using Schauder fix theo rem, the ex istence of the so lut ion of the perturbation problems is g iven.

参考文献/References:

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相似文献/References:

[1]韦金生,朱顺荣.含小参数非线性扰动系统的渐近等价性[J].南京理工大学学报(自然科学版),1998,(03):89.
 Wei Jingsheng Zhu Shunrong.Asymptotic Equivalence of Nonlinear Parametric Systems with a Small Parameter[J].Journal of Nanjing University of Science and Technology,1998,(03):89.

备注/Memo

备注/Memo:
作者简介: 吴建成( 1956- ), 男, 江苏南通人, 教授, 主要研究方向: 应用偏微分方程, E-m ail: Wu jc@ jpu. edu. cn。
更新日期/Last Update: 2006-06-30