Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030129

E.I. Nikulin, N.N. Nefedov, A.O. Orlov

引用次数: 0

Abstract

This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability.

DOI 10.1134/S1061920824030129

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具有 KPZ 非线性的季霍诺夫型反应-扩散-平流系统中周期抛物问题的解的存在性和渐近稳定性

本文研究奇异扰动 Tikhonov 反应-扩散-对流方程系统的时周期解，其非线性包括未知函数梯度的平方（KPZ 非线性）。针对 Neumann 和 Dirichlet 边界条件，构建了解的边界层渐近线。研究既考虑了准单调源的情况，也考虑了无准单调性条件的系统。利用微分不等式的渐近方法证明了解的存在性及其 Lyapunov 渐进稳定性定理。 doi 10.1134/s1061920824030129

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.