{"title":"Inelastic Boltzmann equation driven by a particle thermal bath","authors":"Rafael Sanabria","doi":"10.3934/krm.2021018","DOIUrl":null,"url":null,"abstract":"We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $ \\alpha\\in(0,1) $, under the thermalization induced by a host medium with fixed $ e\\in(0,1] $ and a fixed Maxwellian distribution. When the restitution coefficient $ \\alpha $ is close to 1 we prove existence and uniqueness of global solutions considering the close-to-equilibrium regime. We also study the long-time behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"3 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kinetic and Related Models","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/krm.2021018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $ \alpha\in(0,1) $, under the thermalization induced by a host medium with fixed $ e\in(0,1] $ and a fixed Maxwellian distribution. When the restitution coefficient $ \alpha $ is close to 1 we prove existence and uniqueness of global solutions considering the close-to-equilibrium regime. We also study the long-time behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.
期刊介绍:
KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.