背面发生图灵分岔的临界拉面的非线性对流稳定性：案例研究

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-03 DOI:10.1137/21m1451038

Louis Garénaux

{"title":"背面发生图灵分岔的临界拉面的非线性对流稳定性：案例研究","authors":"Louis Garénaux","doi":"10.1137/21m1451038","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3275-3325, June 2024. <br/> Abstract. We study the asymptotic stability of a front connecting two unstable states. Such a structure typically appears when the stable state behind a Fisher–Kolmogorov–Petrovskii–Piskunov front destabilizes when going through an essential Turing bifurcation, giving rise to oscillating patterns. Despite the instability of both end-states, we obtain for the first time stability of such a structure against suitably localized perturbations, with algebraic temporal decay [math]. To deal with the instability behind the front, we simultaneously control the error in two different norms. In the first norm, enhanced diffusive decay is obtained at a linear level through pointwise resolvent estimates. In the second norm, better suited for nonlinear analysis, we show that the error stays bounded in time by use of mode filters.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Convective Stability of a Critical Pulled Front Undergoing a Turing Bifurcation at Its Back: A Case Study\",\"authors\":\"Louis Garénaux\",\"doi\":\"10.1137/21m1451038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3275-3325, June 2024. <br/> Abstract. We study the asymptotic stability of a front connecting two unstable states. Such a structure typically appears when the stable state behind a Fisher–Kolmogorov–Petrovskii–Piskunov front destabilizes when going through an essential Turing bifurcation, giving rise to oscillating patterns. Despite the instability of both end-states, we obtain for the first time stability of such a structure against suitably localized perturbations, with algebraic temporal decay [math]. To deal with the instability behind the front, we simultaneously control the error in two different norms. In the first norm, enhanced diffusive decay is obtained at a linear level through pointwise resolvent estimates. In the second norm, better suited for nonlinear analysis, we show that the error stays bounded in time by use of mode filters.\",\"PeriodicalId\":51150,\"journal\":{\"name\":\"SIAM Journal on Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Mathematical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/21m1451038\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/21m1451038","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3275-3325 页，2024 年 6 月。摘要。我们研究连接两个不稳定状态的前沿的渐近稳定性。当 Fisher-Kolmogorov-Petrovskii-Piskunov 前沿后面的稳定状态在经历本质图灵分岔时失稳，从而产生振荡模式时，通常会出现这种结构。尽管两种终态都不稳定，但我们首次获得了这种结构在适当局部扰动下的稳定性，并具有代数时间衰减[数学]。为了应对前沿后方的不稳定性，我们同时在两个不同的规范中控制误差。在第一种规范中，通过点解析估计在线性水平上获得增强的扩散衰减。在更适合非线性分析的第二种规范中，我们利用模式滤波器证明误差在时间上是有界的。

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

Nonlinear Convective Stability of a Critical Pulled Front Undergoing a Turing Bifurcation at Its Back: A Case Study

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3275-3325, June 2024.
Abstract. We study the asymptotic stability of a front connecting two unstable states. Such a structure typically appears when the stable state behind a Fisher–Kolmogorov–Petrovskii–Piskunov front destabilizes when going through an essential Turing bifurcation, giving rise to oscillating patterns. Despite the instability of both end-states, we obtain for the first time stability of such a structure against suitably localized perturbations, with algebraic temporal decay [math]. To deal with the instability behind the front, we simultaneously control the error in two different norms. In the first norm, enhanced diffusive decay is obtained at a linear level through pointwise resolvent estimates. In the second norm, better suited for nonlinear analysis, we show that the error stays bounded in time by use of mode filters.

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.