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Inverse problems with nonlocal boundary conditions
(Université de Larbi Ben M’hidi-Oum El Bouaghi, 2021) Alizoui, Imane; Oussaeif, Taki Eddine
In this work, the existence and uniqueness of the solution to three inverse problems are studied. The first problem is dedicated to the study of the existence and the uniqueness of the solution of an inverse problem for a parabolic equation with homogeneous Neumann conditions and additional condition of integral type by application of the fixed point theorem de Schauder and using the Fourier method. In the second problem, the solvability of an inverse hyperbolic Dirichlet equation with additional information in the form of an integral condition is investigated. Where the existence and uniqueness of the solution of the direct problem proved by using the energy inequality method. however, the study of the inverse problem is established by using the fixed point technique. Finally, in the third problem, the oneness of solving the inverse problem of a super-linear parabola with additional integrative information is studied using the same process in the second problem.