Inverse extremum problem for a model of endovenous laser ablation-Reference-Cited by-同舟云学术

Inverse extremum problem for a model of endovenous laser ablation

Published:2020-11-19 Issue:3 Volume:29 Page:467-476
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Kovtanyuk Andrey¹^ORCID,Chebotarev Alexander²,Astrakhantseva Alena³

Affiliation:

1. Klinikum rechts der Isar , Technische Universität München , Ismaningerstr. 22, 81675 München , Germany ; and Far Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok, Russia

2. Institute for Applied Mathematics FEB RAS , Radio st. 7, 690041; and Far Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok , Russia

3. Far Eastern Federal University , Sukhanova st. 8, 690950 , Vladivostok , Russia

Abstract

Abstract An inverse extremum problem (optimal control problem) for a quasi-linear radiative-conductive heat transfer model of endovenous laser ablation is considered. The problem is to find the powers of the source spending on heating the fiber tip and on radiation. As a result, it provides a given temperature distribution in some part of the model domain. The unique solvability of the initial-boundary value problem is proved, on the basis of which the solvability of the optimal control problem is shown. An iterative algorithm for solving the optimal control problem is proposed. Its efficiency is illustrated by a numerical example.

Funder

Ministry of Education and Science of the Russian Federation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0118/pdf

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