
Existence of Solutions to the Heat Convection Equations in a Timedependent DomainExistence of Solutions to the Heat Convection Equations in a Timedependent DomainAA11021653 
"/Kim, Tujin/"Kim, Tujin ,
"/Cao, Daomin/"Cao, Daomin
22
(
2
)
, pp.531

568 , 20150331 , Graduate School of Mathematical Sciences, The University of Tokyo
ISSN:13405705
NCID:AA11021653
Description
In this paper we are concerned with the initial boundary value problems of the heat convection equations in a timedependent 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 timedependent 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 NavierStokes equations with the nonstandard boundary conditions.
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