Research Communication | Open Access
Volume 2019 | Communication ID 2
Volume 2019 | Communication ID 2
| An Inverse Backward Problem for Degenerate two-dimensional parabolic equation |
Khalid Atifi, Khouiti Bouchra
Received |
Accepted |
Published |
Aug 12, 2018 |
Dec 31, 2018 |
Mar 01, 2019 |
Abstract: This paper deals with the determination of an initial condition in degenerate two-dimensional parabolic equation from final observations. This inverse problem can be considered as a problem of minimizing of a cost function J. To solve it, firstly, we give a new theorem which gives the existence and uniqueness of the weak solution of the direct problem. Secondly, to show that the minimization problem and the direct problem are well-posed, we prove that the solution's behavior changes continuously with the initial conditions. Thirdly, we prove the differentiability of the functional J, ...