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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2024 Volume 232, Pages 30–36 (Mi into1264)

Models of cooling and freezing of living biological tissues with a flat ruler applicator

B. K. Buzdov

Institute of Computer Science and Problems of Regional Management – branch of Federal public budgetary scientific establishment "Federal scientific center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", Nal'chik

Abstract: 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

UDC: 519.711.3

MSC: 97M60

DOI: 10.36535/2782-4438-2024-232-30-36



© Steklov Math. Inst. of RAS, 2025