Inverse Problem for Equations of Complex Heat Transfer with Fresnel Matching Conditions

An inverse problem is considered for a system of semilinear elliptic equations that simulate radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The problem consists in finding the right-hand side of the heat equation, which is a linear...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2021-02, Vol.61 (2), p.288-296
Main Author: Chebotarev, A. Yu
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Elliptic functions
Inverse problems
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Radiative heat transfer
Refractivity
Surface matching
Thermodynamics
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Summary:An inverse problem is considered for a system of semilinear elliptic equations that simulate radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The problem consists in finding the right-hand side of the heat equation, which is a linear combination of given functionals from their specified values on the solution. The solvability of the inverse problem is proved without restrictions on smallness. A sufficient condition for the uniqueness of the solution is presented.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542521020056