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JOURNALS // Sibirskii Zhurnal Industrial'noi Matematiki // Archive

Sib. Zh. Ind. Mat., 2023 Volume 26, Number 4, Pages 180–193 (Mi sjim1268)

This article is cited in 1 paper

Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer

A. Yu. Chebotarev, N. M. Park, A. E. Kovtanyuk

Far Eastern Federal University, Far Eastern Center for Mathematical Research, Vladivostok, 690922 Russia

Abstract: We consider an initial-boundary value problem for quasilinear equations of complex heat transfer that model the process of endovenous laser ablation. A priori estimates for the solution are obtained. Results on the global unique solvability of the problem are presented. An algorithm for finding a solution of the initial-boundary value problem is proposed. The efficiency of the algorithm is illustrated by numerical examples. The influence of internal thermal radiation on the behavior of temperature fields is evaluated.

Keywords: quasilinear equations of complex heat transfer, endovenous laser ablation, nonlocal unique solvability, numerical simulation.

UDC: 517.977.5

Received: 01.08.2023
Revised: 29.09.2023
Accepted: 01.11.2023

DOI: 10.33048/SIBJIM.2023.26.412


 English version:
Journal of Applied and Industrial Mathematics, 2023, 17:4, 698–709


© Steklov Math. Inst. of RAS, 2024