2021-11-30T12:45:22Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000399652021-03-02T02:41:35ZExistence of Solutions to the Heat Convection Equations in a Time-dependent DomainKim, Tujin92376Cao, Daomin92377415Heat convection equationstime-dependent domainmixed boundary conditionsexistence.In this paper we are concerned with the initial boundary value problems of the heat convection equations in a time-dependent domain with mixed boundary conditions involving the total pressure of fluid.W e obtain the existence of a weak solution to the problem. By a transformation of unknown functions and a penalty method we connect the problem to an elliptic operator equation for functions defined in the time-dependent domain. Owing to the transformation we do not need to assume that the given data are small enough. This method is also valid for the Navier-Stokes equations with the nonstandard boundary conditions.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2015-03-31application/pdfJournal of mathematical sciences, the University of Tokyo222531568AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/39965/files/jms220202.pdfeng