發(fā)布時(shí)間：2021-07-14 18:54

　　近年來(lái),對(duì)內(nèi)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(dòng)邊值問(wèn)題內(nèi)部層解的研究提供了理論依據(jù).通過(guò)對(duì)奇異攝動(dòng)邊值問(wèn)題狀態(tài)解極限性質(zhì)的深入研究,本文探討了幾類右端不連續(xù)奇異攝動(dòng)邊值問(wèn)題內(nèi)部層解的存在性.內(nèi)部層也稱為空間對(duì)照結(jié)構(gòu),主要分為階梯狀內(nèi)部層和脈沖狀內(nèi)部層兩大類.本文主要討論右端不連續(xù)奇異攝動(dòng)邊值問(wèn)題的階梯狀內(nèi)部層解.它的基本特點(diǎn)是在所討論區(qū)間內(nèi)存在一點(diǎn)t₀（當(dāng)然也可以存在多點(diǎn)t₀）,t₀稱為轉(zhuǎn)移點(diǎn),因?yàn)樵诿總�(gè)轉(zhuǎn)移點(diǎn)的討論完全一樣,所以只討論存在一個(gè)轉(zhuǎn)移點(diǎn)的情況.事先t₀的位置是已知的,需要在漸近解的構(gòu)造過(guò)程中確定y（t₀）.在t₀的某個(gè)小鄰域內(nèi),問(wèn)題的解會(huì)發(fā)生劇烈的結(jié)構(gòu)變化,當(dāng)小參數(shù)趨于零時(shí),解會(huì)趨向于不同的退化解.第一章回顧了奇異攝動(dòng)邊值問(wèn)題的發(fā)展過(guò)程,引入了與本文研究?jī)?nèi)容相關(guān)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(dòng)二階擬線性邊值問(wèn)題,因?yàn)橛叶隧?xiàng)具有不連續(xù)... 

【文章來(lái)源】：華東師范大學(xué)上海市 211工程院校 985工程院校 教育部直屬院校

【文章頁(yè)數(shù)】：92 頁(yè)

【學(xué)位級(jí)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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