Geodesic
About one two-dimensional mathematical model in cryomedicine
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2005), pp. 1-5

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The work shows that in the case of a flat and sufficiently long cryosurgical instrument, the process of heat propagation in biological tissue is modeled by a two-dimensional Stefan-type initial-boundary value problem. The formulation of this problem for a rectangular area is considered. An algorithm for finding approximate values of temperature and position of isothermal surfaces is presented. A solution is given to a “smoothed” problem that approximates the original Stefan problem using a locally one-dimensional method. The resulting nonlinear algebraic systems were solved using Newton's iterative method.
Keywords: cryomedicine, hypothermia, Stefan type problem, two-dimensional initial-boundary value problem 
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B. K. Buzdov; A. K. Buzdov. About one two-dimensional mathematical model in cryomedicine. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2005), pp. 1-5. http://geodesic.mathdoc.fr/item/IZKAB_2005_2_a0/