The Motion of the Front in the Reaction-Advection-Diffusion Problem with Periodic Coefficients

被引：2

作者：

Nikulin, E. I. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Phys, Dept Math, Moscow 119991, Russia

来源：

MOSCOW UNIVERSITY PHYSICS BULLETIN | 2022年 / 77卷 / 05期

基金：

俄罗斯科学基金会;

关键词：

periodic solutions; reaction-advection-diffusion; front; asymptotic stability; method of differential inequalities; upper and lower solutions; internal transition layer; small parameter; CONTRAST STRUCTURES; EXISTENCE;

D O I：

10.3103/S0027134922050113

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper shows the existence and asymptotic Lyapunov stability of solutions with a moving inner layer (front) in a boundary value problem for a singularly perturbed parabolic reaction-advection-diffusion equation with the periodicity condition in time. In addition, the existence of solutions of this type for the corresponding initial boundary value problem is proved and a sufficient condition for their attraction to a periodic solution is proposed. For each problem, an asymptotic approximation of the solution is constructed and the existence and uniqueness theorems for such a solution with the constructed asymptotic behavior based on the asymptotic method of differential inequalities are proved.

引用

页码：747 / 754

页数：8

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