Research
Communication | Open Access
Volume 2021 | Communication ID 62
Volume 2021 | Communication ID 62
Identification of source terms in heat equation with dynamic boundary conditions |
El Mustapha Ait Ben Hassi, Salah-Eddine Chorfi, Lahcen Maniar
Received |
Accepted |
Published |
May 12, 2021 |
May 20, 2021 |
July 15, 2021 |
Abstract: We study an inverse parabolic problem of simultaneously identifying two source terms in the heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov [3], 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. Then the Lipschitz continuity of the gradient of the cost functional is established. Next, the existence and the uniqueness of a quasi-solution are also investigated. In particular, we present a sufficient ...