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Identification of source terms in heat equation with dynamic boundary conditions.

Authors :
Ait Ben Hassi, El Mustapha
Chorfi, Salah‐Eddine
Maniar, Lahcen
Source :
Mathematical Methods in the Applied Sciences. 3/15/2022, Vol. 45 Issue 4, p2364-2379. 16p.
Publication Year :
2022

Abstract

We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is analyzed, especially a gradient formula of the functional is proved and given in terms of the solution of an adjoint problem. Next, the existence and uniqueness of a quasi‐solution are also investigated. Finally, the numerical reconstruction of some heat sources in a 1‐D equation is presented to show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01704214
Volume :
45
Issue :
4
Database :
Academic Search Index
Journal :
Mathematical Methods in the Applied Sciences
Publication Type :
Academic Journal
Accession number :
155106573
Full Text :
https://doi.org/10.1002/mma.7933