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JOURNALS // Dal'nevostochnyi Matematicheskii Zhurnal // Archive

Dal'nevost. Mat. Zh., 2022 Volume 22, Number 2, Pages 143–149 (Mi dvmg477)

Theoretical analysis of cloaking problem for 3D model of heat conduction

G. V. Alekseev

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok

Abstract: The direct and extremal problems for the 3D heat conduction model are formulated which are associated with designing spherical thermal cloaking devices. The solvability of both problems is proved. An optimality system is constructed that describes the necessary conditions for an extremum. Some properties of optimal solutions which are consequence of the structure of the optimality system are established.

Key words: inverse problem, heat conduction, solvability, optimality system.

UDC: 517.95

MSC: Primary 35Q79; Secondary 35Q93

Received: 16.06.2022

Language: English

DOI: 10.47910/FEMJ202214



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