具有奇异摄动Neumann边界条件的奇异摄动积分微分方程的边值问题

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

Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI:10.1134/S1061920823030081

N. N. Nefedov, A. G. Nikitin, E. I. Nikulin

{"title":"具有奇异摄动Neumann边界条件的奇异摄动积分微分方程的边值问题","authors":"N. N. Nefedov, A. G. Nikitin, E. I. Nikulin","doi":"10.1134/S1061920823030081","DOIUrl":null,"url":null,"abstract":"<p> We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"375 - 381"},"PeriodicalIF":1.7000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition\",\"authors\":\"N. N. Nefedov, A. G. Nikitin, E. I. Nikulin\",\"doi\":\"10.1134/S1061920823030081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given. </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 3\",\"pages\":\"375 - 381\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823030081\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823030081","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

考虑一类奇异摄动积分微分方程的边值问题，该方程描述了非局部相互作用下的平稳反应扩散过程。该问题的主要特征是存在一个奇摄动诺伊曼条件，描述边界上的强流动。证明了边界层解的存在性，构造了它的渐近逼近，并建立了它的渐近Lyapunov稳定性。给出了实例说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition

We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.