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1.
§ 1  IntroductionA class of singularly perturbed boundary value problems were studied by Mo[1~ 6] .Now we consider the following singularly perturbed nonlinear boundary value problem ofthe formεd2 ydx2 =f(x,y,y′) ,  0 相似文献   

2.
In this paper,we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation,the solution is shown to exhibit multiple layer behavior.According to different layers and by introducing extended variable,we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.  相似文献   

3.
高阶拟线性椭圆型方程奇摄动问题   总被引:2,自引:0,他引:2  
本文利用微分不等式和多重尺度,研究了一个高阶椭圆型偏微分方程摄动边值问题,并得到了一致有效的渐近展开式。  相似文献   

4.
奇摄动非线性系统初值问题的套层解   总被引:8,自引:0,他引:8  
本文研究一类二阶非线性系统的初值问题的奇摄动,揭示了其解呈现双重初始层的性质,通过引进不同量级的伸长变量,得到解的一致有效的渐近展开式。  相似文献   

5.
This paper is concerned with boundary and corner layer behavior of the singularly perturbed Robin boundary value problem(RP) for the second-order nonlinear differential equations. The existence and asymptotic estimate of solutions of (RP) is discussed by appropriately constructing the bounding functions and using the theory of differential inequality.  相似文献   

6.
倪明康  丁海云 《数学杂志》2011,31(3):488-494
本文研究了不满足Tikhnov定理中稳定性要求的一类常微分方程奇摄动边值问题.利用边界层函数法以及微分不等式理论,分别构造了渐进解的形式和证明了解的存在性和渐近解一致有效性并进行了余项估计,得出了该类问题边界层代数式衰减的结论.  相似文献   

7.
非线性积分微分方程组奇摄动边值问题   总被引:2,自引:0,他引:2  
本文讨论含积分算子的非线性微分方程组Robin边值问题的奇摄动,在适当假设条件下通过对角化技巧,利用逐步逼近法证明了解的存在,并得到直到O(ε^N+1)的按范数界限的一致有效估计。  相似文献   

8.
9.
§ 1 IntroductionSince 1 970 the perturbed boundary value problems for functional differential equationshave been derived in many fields,such as biology,physics,optimal control and e-conomies[1 ] .Some works on studying it have appeared,for example references[2~ 6] .Inthis paper,we study a kind of singularly perturbed boundary value problems for Volterrafunctional differential equations:εx″(t) =f(t,x(t) ,[Tx] (t) ,x(t-τ) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,(1 )x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,ax(1 )…  相似文献   

10.
In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.  相似文献   

11.
Considerasingularlyperturbedproblemforhigherorderselnilinearequationswhereeisasmallpositiveparameter,ndenotesaboundedregioninRe,whereonsignifiesasmoothboundaryofn,misaintegerandjk,gi,k,j=0,'',in--1,aresufficientlysmoothfunctionswithregardtotheirvariablesincorrespondenceranges.Modealwiththesingularperturbationforthesecondorder'ellipticequations[1],[2],thefourthorderequations[3]l[4]andaclassofhigherorderequations[5].Inthispaperttheauthorsconsiderthesingularperturbationforevenmoregeneralhigheror…  相似文献   

12.
程燕 《数学杂志》2005,25(1):25-29
本文运用了边界层函数构造了一类半线性奇摄动椭圆型方程边值问题解的渐近展开式,并证明了该展开式达到任一精度的一致有效性.  相似文献   

13.
本文研究了具有非局部反应扩散方程的奇摄动问题。利用比较原理,讨论了相应问题解的存在唯一性及其渐近性态。  相似文献   

14.
In this paper, we consider the solvability for a singularly perturbed Robin problem of semi-linear differential system. Using the boundary layer corrective method, the formal asymptotic solution is constructed. Finally, the uniform validity of such asymptotic expansions solution is proved.  相似文献   

15.
讨论了一类半线性奇摄动边值问题,构造了问题的具有代数型特点的左右边界层函数和内部角层函数,利用微分不等式理论证明了问题解的存在性,得到了解的渐近估计,给出了该类问题的一般性结论.并且将结论应用于一类燃烧问题的模型,得到了该模型的渐近估计.对有关文献的相关问题及其结果都作了相应的推广.  相似文献   

16.
本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.  相似文献   

17.
ConsidertheboundaryvalueproblemtothesingularlyperturbednonlinearsystemintheformofwhereEisasmallpositiveparameter,y=(yi,'..)y.),f=(fi,...)fn),A=(Al,'',A.)andB=(BI,sn).MohasdiscussedtheseDroblemsundervarioussituationsusingthemethodofdifferentialinequalities[1--'].Inthispaperweconsiderthecaseoffi.:(0,y,y')=0anduseaclassofnewboundarylayerfunctions.TheoremAssumethat(a)fi(x,y,z)Hfi(x,yi,'',yn,if)''jz.)eC'{xE[~l,1],yie[di,ei],ifER}andtherearepositivenondecreasingcontinuousfunctionsif,i=1,2,'…  相似文献   

18.
拟线性积分微分方程系统的奇摄动边值问题   总被引:5,自引:0,他引:5  
本文研究高维拟线性积分微分方程系统边值问题的奇摄动,在适当的条件下,利 用渐近分析方法和对角化技巧,证得解的存在性,同时给出解的渐近展开式及其相应的 余项估计.  相似文献   

19.
SINGULARPERTURBATIONOFROBINBOUNDARYVALUEPROBLEMFORTHIRDORDERNONLINEARSYSTEMWITHBOUNDARYPERTURBATION(黄晓秋)福建师范大学福清分校,邮编:350300H...  相似文献   

20.
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