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 The News of Altai State University
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Content of 1(31) 2004
Mathematics and Computer Science
Physics
 
1(31)2004
Mathematics and Computer Science

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S.A. Sazhenkov

Method of kinetic equation for the Darcy#Stefan problem on phase transitions in a porous ground

The Cauchy problem for the Darcy#Stefan model, which describes phenomena of freezing and thawing of viscous incompressible fluid filtering through a porous ground, is considered in the presence of nonlinear temperature-depending buoyancy forces. The main result of the paper consists of the theorem on existence of entropy solution to the problem.
The proof of the theorem is based on application of the method of kinetic equation which allows to reduce originally nonlinear problems to linear forms with additional kinetic variables.
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