Existence of Solutions to the Heat Convection Equations in a Time-dependent Domain with Mixed Boundary Conditions

Journal of Mathematical Sciences

Cao, Daomin¹  Kim, Tujin¹ 

关键词: Heat convection equations;    time-dependent domain;    mixed boundary conditions;    existence.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Inthispaperweareconcernedwiththeinitialboundaryvalueproblemsoftheheatconvectionequationsinatime-dependentdomainwithmixedboundaryconditionsinvolvingthetotalpressureoffluid.Weobtaintheexistenceofaweaksolutiontotheproblem.Byatransformationofunknownfunctionsandapenaltymethodweconnecttheproblemtoanellipticoperatorequationforfunctionsdefinedinthetime-dependentdomain.Owingtothetransformationwedonotneedtoassumethatthegivendataaresmallenough.ThismethodisalsovalidfortheNavier-Stokesequationswiththenonstandardboundaryconditions.

【 授权许可】

Unknown