{"title":"Strong Convergence of Solutions and Attractors for Reaction-Diffusion Equations Governed by a Fractional Laplacian","authors":"Jiaohui Xu, Tomás Caraballo, José Valero","doi":"10.1007/s00245-025-10242-w","DOIUrl":null,"url":null,"abstract":"<div><p>A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to <span>\\(1\\)</span>. Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10242-w.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10242-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to \(1\). Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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