Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Суковатов К.Ю.## Mathematical model of phase transfer in four-layer mediumThis paper is devoted to development of mathematical model of phase transfer in four-layer medium. It is known that there is a connection between linear hyperbolic and nonlinear parabolic operators of heat transfer. This connection allows to obtain solutions of nonlinear parabolic equation of heat transfer with variable coefficient of heat conductivity by solving the linear hyperbolic equation of heat transfer with constant coefficient. Usage of hyperbolic equations of heat transfer permit to model process of heat transfer with finite speed. Analytical solutions of Stefan problem were obtained for cases with coefficient of heat conductivity with linear dependence from temperature and with coefficient of heat conductivity as a nonlinear function of temperature. Proposed model can be used, for example, to model the process of freezing of soil under the snow.
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