近年來,對內部層解的研究已取得了非常深入的成果,從而為右端不連續(xù)奇異攝動邊值問題內部層解的研究提供了理論依據.通過對奇異攝動邊值問題狀態(tài)解極限性質的深入研究,本文探討了幾類右端不連續(xù)奇異攝動邊值問題內部層解的存在性.內部層也稱為空間對照結構,主要分為階梯狀內部層和脈沖狀內部層兩大類.本文主要討論右端不連續(xù)奇異攝動邊值問題的階梯狀內部層解.它的基本特點是在所討論區(qū)間內存在一點t₀（當然也可以存在多點t₀）,t₀稱為轉移點,因為在每個轉移點的討論完全一樣,所以只討論存在一個轉移點的情況.事先t₀的位置是已知的,需要在漸近解的構造過程中確定y（t₀）.在t₀的某個小鄰域內,問題的解會發(fā)生劇烈的結構變化,當小參數(shù)趨于零時,解會趨向于不同的退化解.第一章回顧了奇異攝動邊值問題的發(fā)展過程,引入了與本文研究內容相關的一些基本定義和引理,介紹了本文的工作和創(chuàng)新之處.第二章研究了帶有Neumann和Dirichlet邊界條件的奇異攝動二階擬線性邊值問題,因為右端項具有不連續(xù)... 

【文章來源】：華東師范大學上海市 211工程院校 985工程院校 教育部直屬院校

【文章頁數(shù)】：92 頁

【學位級別】：博士

【文章目錄】：
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



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