{"title":"Stability and decay rate of space-periodic solutions to porous medium equations with convection","authors":"Yechi Liu","doi":"10.1016/j.physleta.2024.130095","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we discuss the asymptotic stability of periodic solutions in the spacial variable to porous medium equations with convection. At first, based on the argument method of the <em>ω</em>-limit set theory in ordinary differential equations, we obtain that the periodic solution with a periodic initial function exponentially decays to its average. Then, using this result, the anti-derivative technique and energy estimates, we prove the asymptotic stability of the periodic solution and give a time decay rate.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"529 ","pages":"Article 130095"},"PeriodicalIF":2.3000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960124007898","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we discuss the asymptotic stability of periodic solutions in the spacial variable to porous medium equations with convection. At first, based on the argument method of the ω-limit set theory in ordinary differential equations, we obtain that the periodic solution with a periodic initial function exponentially decays to its average. Then, using this result, the anti-derivative technique and energy estimates, we prove the asymptotic stability of the periodic solution and give a time decay rate.
期刊介绍：
Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.
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