Inverse coefficient super-linear problem for a time fractional parabolic equation under integral overdetermination conditions

Abstract

In this paper, we investigate the inverse problem of the determining the right-hand side of a nonlinear fractional parabolic equation with integral overdetermination condition. For the solvability of the direct problem we use the energy inequality method also known as the methode of functional analysis or the method of a priori estimates, this method has a higher character in that the existence theorem can be derived from the solution of the problem posed, begining with the uniqueness theorem. The most difficult aspect of this method is selecting the functional spaces E and F and for the unique solvability of the iverse problem is estblished under suitable conditions. The fixed point theoremis used to establish the existence and uniqueness of the solution to the inverse problem based on the data, this inverse problem appears frequently in engineering and physics modeling of various phenomena. Sismology, medicine, continuous casting, fusion welding, oil and gas production during drilling and well operation.