{"title":"Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations","authors":"Georgy Kitavtsev, Roman M. Taranets","doi":"10.3233/asy-231884","DOIUrl":null,"url":null,"abstract":"We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having non-homogeneous in space and time source terms with zero mean. In dimensions two and three, we determine critical values of porous medium exponent for the asymptotic H1-convergence of the solutions to a unique non-homogeneous positive steady state generally to hold.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"39 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-231884","RegionNum":4,"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
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having non-homogeneous in space and time source terms with zero mean. In dimensions two and three, we determine critical values of porous medium exponent for the asymptotic H1-convergence of the solutions to a unique non-homogeneous positive steady state generally to hold.
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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