Contrast Structures with a Multizone Internal Layer

被引：2

作者：

Butuzov, V. F. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 119991, Russia

来源：

AUTOMATIC CONTROL AND COMPUTER SCIENCES | 2018年 / 52卷 / 07期

基金：

俄罗斯基础研究基金会;

关键词：

singularly perturbed equation; internal transition layer; step-like and spike-like contrast structures; asymptotic expansion of solution;

D O I：

10.3103/S0146411618070052

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A boundary value problem for a singularly perturbed second-order differential equation is considered in two cases, in each of which one of the roots of the degenerate equation is double. In the first case, a narrow internal layer is proven to be formed where there is a rapid transition of the solution from the double root of the degenerate equation to a simple root; in the second case, the solution is proven to have a spike in the internal layer. Such solutions are called step-like contrast structures and spike-like contrast structures, respectively. In each case, the asymptotic expansion of the contrast structure is constructed. It significantly differs from the known expansion when all roots of the degenerate equation are simple; in particular, the internal layer turns out to be multizone.

引用

页码：745 / 761

页数：17