奇异摄动边值问题的渐近展开
The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems
-
摘要: 本文研究了奇异摄动边值问题:εy"=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε),其中ε是一个正小参数.在条件fy(0,y,0)≥m0(>0),fy(1,y,0)≥m0和fy(t,y,ε)≥0之下.我们证明了解的存在唯一性,并给出了解的一致有效渐近展开式,从而改进了已有的结果.Abstract: In this paper we study the singularly penurbed boundary value problem:εy"=f(t,y,ε), y(0)=ξ(ε),y(1)=η(ε), where ε is a positive small parameter In the conditions:fy(0,y,0)≥m0,fy(1,y,0)≥m0 and fy(t,y,ε)≥0, we prove the existences, and uniformly valid asymptotic expansions of solutions for the given boundary value problems, and hence we improve the existing results.
-
[1] Fife,P.C.,Semilinear elliptic boundary value problems with small parameters,Arch.Ration Mach.Anal.,52,3(1973),205-232. [2] Howes,F.A.,A class of boundary value problems whose solutions possess angular limiting behavior,Rocky Min.J Math.,6(1976),591-607. [3] Howes,F.A.,Singularly perturbed semilinear systems,Stud Appl.Math.,61(1979),185-209. [4] O'Donnell,M.A.,Boundary and corner layer behavior in singularly perturbed semilinear systems boundary value problems,SIAM J.Math.Anal.,2(1984),317-332. [5] 章国华、刘光旭,奇摄动半线性系统的边界层和角层性质,应用数学和力学,5,3 (1984),337-344. [6] 林宗池、倪守平,算子与边界双摄动的非线性方程边值问题的奇摄动,数学杂志,3,3 (1983),205-216. [7] Nagumo,M.,Über die differentialgleichung y"=f(x,y,y'),Proc.Phys.Math.Soc.Japan,19(1937),861-866. -
点击查看大图
计量
- 文章访问数: 1661
- HTML全文浏览量: 38
- PDF下载量: 542
- 被引次数: 0
下载:
