首页 > 硕士 > 理学 > 正文

一类非线性抛物型方程解的多重性

Multiplicity of Solutions of a Nonlinear Parabolic Equation

作者: 专业:应用数学 导师:金正国 年度:2010 学位:硕士  院校: 大连理工大学

Keywords

Parabolic equations, Dirichlet boundary condition, Multiplicity of solutions, Nonlinear, Variational reduction method

        偏微分方程解的存在性和多重性的研究,是偏微分方程理论的重要组成部分。研究带有边值条件的偏微分方程解的存在性和多重性,是偏微分方程理论研究的重要课题。本文研究了在有界区域上,满足Dirichlet边界条件的一类非线性抛物型方程Lu-Dtu+g(u)=f(x,t)方程解的多重性,同时也讨论了方程解的多重性与非线性扰动项之间的关系。第一部分,引言。第二部分,介绍本文将要用到的一些重要的定义和定理。第三部分,利用变分法和压缩映射原理,把无限维空间问题转化为有限维空间问题。第四部分,研究方程解的多重性与非线性扰动项之间的关系。第五部分,结论。
    The existence and multiplicity of solutions are important components of the theory of partial differential equation.The researches for existence and multiplicity of solutions under boundary conditions are important subjects of partial differential equation.We investigate the existence of multiple solutions of the nonlinear equation under Dirichlet boundary condition onΩ, Lu-Dtu+g(u)=f(x,t). We also discuss a relation between multiplicity of solutions and the nonlinear perturbation of the equation.In section 1, introduction is given.In section 2, we introduce some important definitions and theorems.In section 3, we use variational reduction method and contraction mapping theorem to transform the problem from an infinite dimensional’one to a finite dimensional one.In section 4, we reveal a relation between multiplicity of solutions and the nonlinear perturbation of the equation.In section 5, we give the conclusion.
        

一类非线性抛物型方程解的多重性

摘要4-5
Abstract5
引言7-11
1 预备知识11-17
2 变分法17-21
3 解的多重性与非线性扰动项21-29
    3.1 扰动项满足a>(b(λ_(01)+λ_(02))-2λ_(01)λ_(02))/(2b-(λ_(01)+λ_(02)))22-24
    3.2 扰动项满足a<(b(λ_(01)+λ_(02))-2λ_(01)λ_(02))/(2b-(λ_(01)+λ_(02)))24-26
    3.3 扰动项满足a=(b(λ_(01)+λ_(02))-2λ_(01)λ_(02))/(2b-(λ_(01)+λ_(02)))26-29
结论29-31
参考文献31-35
攻读硕士学位期间发表学术论文情况35-37
致谢37-40
        下载全文需50


本文地址:

上一篇:宏/微定位平台控制系统设计
下一篇:基于曲面约束的自适应B样条曲线拟合

分享到: 分享一类非线性抛物型方程解的多重性到腾讯微博           收藏
评论排行
公告