Study of an inverse problem that models the detection of corrosion in metalic plate whose lower part is embedded

In this work, we will study an inverse problem to determine corrosion in an inaccessible location of a metalic plate. Our study area is inside the plate metalic plate whose lower part is embedded therefore inacssecible. We will perform measurements on the upper part of the plate, which is not in contact with the ground. For this, we will send an electric field on this part and take measurements. This problem is modeled by a Laplace problem with mixed presence of an unknown term in the boundary conditions this term is an unknown function which can take several forms. It is this function that we will detect the presence or absence of corrosion inside the tube and we will then follow our steps to the top edge of the field information on the evolution of this corrosion. We will first formulate our problem which is an inverse problem and we will make a theoretical study and we will that this problem has a unique solution also this solution is stable. After, we will solve this problem by constructing an iterative algorithm which gives problems that will cross a series of impedance functions which determines the rate of corrosion. Finally we study the convergence and we will then make a numerical application