Models of cooling and freezing of living biological tissues with a flat ruler applicator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 30-36
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In this work, we construct new mathematical models of cooling and freezing of living biological tissue with a flat, long ruler applicator located on its surface. The models are two-dimensional boundary-value problems (including Stefan-type problems) and have applications in cryosurgery. The method of numerical study of these problems is based on smoothing discontinuous functions and applying locally one-dimensional difference schemes to “smoothed” problems without explicitly identifying the boundaries of the influence of cold and the boundaries of the phase transition.
Keywords:
mathematical model, cryomedicine, Stefan type problem
@article{INTO_2024_232_a2,
author = {B. K. Buzdov},
title = {Models of cooling and freezing of living biological tissues with a flat ruler applicator},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {30--36},
publisher = {mathdoc},
volume = {232},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/}
}
TY - JOUR AU - B. K. Buzdov TI - Models of cooling and freezing of living biological tissues with a flat ruler applicator JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2024 SP - 30 EP - 36 VL - 232 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/ LA - ru ID - INTO_2024_232_a2 ER -
%0 Journal Article %A B. K. Buzdov %T Models of cooling and freezing of living biological tissues with a flat ruler applicator %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2024 %P 30-36 %V 232 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/ %G ru %F INTO_2024_232_a2
B. K. Buzdov. Models of cooling and freezing of living biological tissues with a flat ruler applicator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 30-36. http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/