几类右端不连续奇异摄动边值问题的研究
发布时间：2021-07-14 18:54
近年来,对内部层解的研究已取得了非常深入的成果,从而为右端不连续奇异摄动边值问题内部层解的研究提供了理论依据.通过对奇异摄动边值问题状态解极限性质的深入研究,本文探讨了几类右端不连续奇异摄动边值问题内部层解的存在性.内部层也称为空间对照结构,主要分为阶梯状内部层和脉冲状内部层两大类.本文主要讨论右端不连续奇异摄动边值问题的阶梯状内部层解.它的基本特点是在所讨论区间内存在一点t0（当然也可以存在多点t0）,t0称为转移点,因为在每个转移点的讨论完全一样,所以只讨论存在一个转移点的情况.事先t0的位置是已知的,需要在渐近解的构造过程中确定y（t0）.在t0的某个小邻域内,问题的解会发生剧烈的结构变化,当小参数趋于零时,解会趋向于不同的退化解.第一章回顾了奇异摄动边值问题的发展过程,引入了与本文研究内容相关的一些基本定义和引理,介绍了本文的工作和创新之处.第二章研究了带有Neumann和Dirichlet边界条件的奇异摄动二阶拟线性边值问题,因为右端项具有不连续...
【文章来源】：华东师范大学上海市 211工程院校 985工程院校 教育部直属院校
【文章页数】：92 页
【学位级别】：博士
【文章目录】：
中文摘要
Abstract
1 Introduction
1.1 Background
1.1.1 Tikhonov’s theorem
1.1.2 The method of boundary functions. Vasilieva Theorem
1.1.3 Contrast structure
1.2 Motivation
1.3 Main results
2 Contrast structure in a singularly perturbed second-order equation with the mixed boundary condition
2.1 Formulation of the problem
2.2 Attached system
2.3 Asymptotic representation of the solution
2.4 The regular terms of asymptotic representation
2.5 Construction of the internal transition layer
2.6 Construction of left boundary functions
2.7 Construction of right boundary functions
2.8 Existence of solution
2.9 Numerical example
3 Internal layer for a singularly perturbed second-order equation with the Robin boundary condition
3.1 Formulation of the problem
3.2 Attached system
3.3 Asymptotic approximation of the solution
3.4 The regular terms of asymptotic representation
3.5 Construction of the internal transition layer
3.6 Existence of solution
3.7 Numerical example
4 Contrast structure in the reactions-diffusion-advection equation with the Robin boundary condition
4.1 Formulation of the problem
4.2 Main conditions
4.3 Auxiliary system
4.4 Construction the asymptotics solution of the type of contrast structure
4.5 Existence of solution
4.6 Numerical example
5 Internal layer for a system of singularly perturbed equations with the Robin boundary condition
5.1 Formulation of the problem
5.2 Asymptotic representation of the solution
5.3 The regular part of the asymptotic representation
5.4 Transition layer functions
5.5 Higher-order transition layer functions
5.6 Matching of asymptotic representations
5.7 Boundary functions
5.8 Asymptotic solution approximation
5.9 Existence of solution
5.10 Numerical example
Conclusion
References
Publications
Acknowledgements
Resume
本文编号：3284698
【文章来源】：华东师范大学上海市 211工程院校 985工程院校 教育部直属院校
【文章页数】：92 页
【学位级别】：博士
【文章目录】：
中文摘要
Abstract
1 Introduction
1.1 Background
1.1.1 Tikhonov’s theorem
1.1.2 The method of boundary functions. Vasilieva Theorem
1.1.3 Contrast structure
1.2 Motivation
1.3 Main results
2 Contrast structure in a singularly perturbed second-order equation with the mixed boundary condition
2.1 Formulation of the problem
2.2 Attached system
2.3 Asymptotic representation of the solution
2.4 The regular terms of asymptotic representation
2.5 Construction of the internal transition layer
2.6 Construction of left boundary functions
2.7 Construction of right boundary functions
2.8 Existence of solution
2.9 Numerical example
3 Internal layer for a singularly perturbed second-order equation with the Robin boundary condition
3.1 Formulation of the problem
3.2 Attached system
3.3 Asymptotic approximation of the solution
3.4 The regular terms of asymptotic representation
3.5 Construction of the internal transition layer
3.6 Existence of solution
3.7 Numerical example
4 Contrast structure in the reactions-diffusion-advection equation with the Robin boundary condition
4.1 Formulation of the problem
4.2 Main conditions
4.3 Auxiliary system
4.4 Construction the asymptotics solution of the type of contrast structure
4.5 Existence of solution
4.6 Numerical example
5 Internal layer for a system of singularly perturbed equations with the Robin boundary condition
5.1 Formulation of the problem
5.2 Asymptotic representation of the solution
5.3 The regular part of the asymptotic representation
5.4 Transition layer functions
5.5 Higher-order transition layer functions
5.6 Matching of asymptotic representations
5.7 Boundary functions
5.8 Asymptotic solution approximation
5.9 Existence of solution
5.10 Numerical example
Conclusion
References
Publications
Acknowledgements
Resume
本文编号：3284698
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