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arXiv · 2105.14518

Identification of source terms in heat equation with dynamic boundary conditions

E. M. Ait Ben Hassi·S. E. Chorfi·L. Maniar
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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.

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E. M. Ait Ben Hassi, S. E. Chorfi, L. Maniar. 2021-05-30. Identification of source terms in heat equation with dynamic boundary conditions. https://doi.org/10.1002/mma.7933

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