{"title":"Existence and stability of steady states of reaction–diffusion equation with spatiotemporal memory","authors":"Shu Li , Binxiang Dai , Hao Wang","doi":"10.1016/j.aml.2024.109323","DOIUrl":null,"url":null,"abstract":"<div><div>This paper focuses on a reaction–diffusion equation with spatiotemporal memory and Dirichlet boundary condition. We prove the existence of positive steady-state solutions through local and global bifurcation theory and provide the conditions for the stability of positive steady-state solutions. Our general results are applied to a diffusive logistic population model with spatiotemporal memory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109323"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003434","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
This paper focuses on a reaction–diffusion equation with spatiotemporal memory and Dirichlet boundary condition. We prove the existence of positive steady-state solutions through local and global bifurcation theory and provide the conditions for the stability of positive steady-state solutions. Our general results are applied to a diffusive logistic population model with spatiotemporal memory.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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