{"title":"Gradient Decay in the Boltzmann Theory of Non-isothermal Boundary","authors":"","doi":"10.1007/s00205-024-01956-2","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging to <span> <span>\\(W^{1,p}_x\\)</span> </span> for any <span> <span>\\(p<3\\)</span> </span>. We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially quickly as <span> <span>\\(t \\rightarrow \\infty \\)</span> </span>.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00205-024-01956-2","RegionNum":1,"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
We consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging to \(W^{1,p}_x\) for any \(p<3\). We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially quickly as \(t \rightarrow \infty \).
期刊介绍：
The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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