Geodesic
On one model of freezing biological living tissues
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 14-18

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In this paper, we present a new mathematical model of freezing a living biological tissue by a cryoapplicator and a method for its numerical study based on the use of local one-dimensional difference schemes. The model is a three-dimensional three-phase boundary-value Stefan-type problem and has applications in cryosurgery. A special nonlinear dependence of heat sources on the unknown temperature field allows one to take into account the spatial effect of heat localization.
Keywords: mathematical modeling, cryomedicine, cryobiology, Stefan problem. 
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     author = {B. K. Buzdov},
     title = {On one model of freezing biological living tissues},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {14--18},
     publisher = {mathdoc},
     volume = {190},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_190_a1/}
}
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B. K. Buzdov. On one model of freezing biological living tissues. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 14-18. http://geodesic.mathdoc.fr/item/INTO_2021_190_a1/