季霍诺夫型反应扩散系统的周期抛物线问题解的存在性、渐近性和李亚普诺夫稳定性

IF 0.6 4区数学 Q3 MATHEMATICS Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s000143462401022x

N. N. Nefedov

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引用次数: 0

摘要

摘要我们研究了反应扩散方程奇异扰动系统在快速方程和慢速方程情况下的一类新的时间周期解，这些方程通常被称为 Tikhonov 型系统。构建了解的边界层渐近线，证明了具有该渐近线的解的存在性，并得到了这些被视为相应初-轫值问题解的解的 Lyapunov 渐近稳定性条件。

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Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems

Abstract

We study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems are obtained.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.