{"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}
引用次数: 0
Abstract
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.
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.
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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.
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