带德里赫特边界条件的 SKT 模型稳态的莫尔斯指数

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-30 DOI:10.1137/23m1627705

Kousuke Kuto, Homare Sato

{"title":"带德里赫特边界条件的 SKT 模型稳态的莫尔斯指数","authors":"Kousuke Kuto, Homare Sato","doi":"10.1137/23m1627705","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5386-5408, August 2024. <br/> Abstract. This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Morse Index of Steady-States to the SKT Model with Dirichlet Boundary Conditions\",\"authors\":\"Kousuke Kuto, Homare Sato\",\"doi\":\"10.1137/23m1627705\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5386-5408, August 2024. <br/> Abstract. This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index.\",\"PeriodicalId\":51150,\"journal\":{\"name\":\"SIAM Journal on Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-30\",\"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/10.1137/23m1627705\",\"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/10.1137/23m1627705","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 4 期，第 5386-5408 页，2024 年 8 月。摘要本文论述了具有 Dirichlet 边界条件的 SKT 模型的全交叉扩散极限扰动稳态的稳定性分析。我们之前的研究结果表明，正稳态包括从三元解分叉的小共存型分支和从小共存型分支上的点分叉的隔离型分支。本文显示了分支上稳态的莫尔斯指数，并构建了每个稳态周围的局部不稳定流形，其维度等于莫尔斯指数。

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

Morse Index of Steady-States to the SKT Model with Dirichlet Boundary Conditions

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5386-5408, August 2024.
Abstract. This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index.

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.