一类高阶椭圆型偏微分方程的奇摄动  

THE SINGULAR PERTURBATION FOR A CLASS OF HIGHER ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

作　　者：莫嘉琪[1] 

机构地区：[1]安徽师范大学

出　　处：《应用数学学报》1993年第1期114-120,共7页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金

摘　　要：今考虑如下奇摄动问题:其中ε为正的小参数,Ω为R^n中的有界域,Ω为Ω的边界,a,b均为正常数,φi(x),i=1,2,3,为充分光滑的函数,Δ为Laplace算子. 本文主要是利用微分不等式理论来研究上述问题解的渐近性态.近年来,利用微分不等式来解决一类常微分方程奇摄动问题已有较深入的研究(例如参见[1]-[5],[9]-A calss of singularly perturbed boundary value problems for a higher order elliptic par-tial differential equation is considered. The problem is: ε~2(Δ~3u — bΔu) — aΔ~2u + abu = 0,x≡(x_1,…,x_n) ∈Ω,u, Δu, Δ~2u be defined on ?Ω, where ε is a small positive parameter, a and b arepositive constants, Ω denotes a bounded region in R^n and ?Ω signifies the smoothboundary of Ω. Using the comparison theorem and introducing multiple variablesand a local coordinate system, the uniformly valid asymptotic solution possessingboundary layer correction terms of the original problem is obtained.

关 键 词：椭圆型方程 奇摄动 偏微分方程 

分 类 号：O175.25[理学—数学]