Geodesic
Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 180-193

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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, numerical simulation.
Mots-clés : endovenous laser ablation, nonlocal unique solvability 
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     author = {A. Yu. Chebotarev and N. M. Park and A. E. Kovtanyuk},
     title = {Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {180--193},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a11/}
}
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A. Yu. Chebotarev; N. M. Park; A. E. Kovtanyuk. Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 180-193. http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a11/