Study of some identification problems by using the Sentinel method

Abstract

This thesis aims to study of various kinds of some identification problems by the use of the sentinel method which is introduced by Jacques Louis Lions. We apply this method for the first time in order to identify parameters and coefficients in some identification problems. Actually, We identify the potential coefficient in the wave equation with incomplete data, the bulk modulus coefficient in the acoustic equation with incomplete data, the potential coefficient in the Schrodinger equation with an incomplete initial condition, and the identification of the diffusion coefficient in the diffusion equation with incomplete data. This method is based on three considerations, a state equation, a state observation, and a functional stationary to certain parameters. The existence of this functional is related to solving an optimal control problem. The determination of these coefficients is crucial for understanding and predicting the behavior of many physical and biological systems.