İkinci dereceden parabolik ve hiperbolik denklemler için ters problemler

Inverse problems for partial differential equation arise when solving many problems of mathematical physics and engineering. An inverse problem is a problem where a source term or some of coefficients of a partial differential equation modeling the appropriated process is unknown. To find the unknown solution and the unknown coefficient or resource term of such a problem, additional conditions will need to be provided. Such conditions may, for example, include partial information of the unknown fields (e.g., temperature) resulting from sensor(experimental) data at distinct points in the domain and time. In this work, our aim is to study the problem of existence and uniqueness of variousinverse problems for second order parabolic and hyperbolic equations. We firstly consider the determination of the initial temperature distribution of heat equations from the final data. We study the problem of identification of the unknown source function of inhomogeneous heat equation. Then we study inverse problems of identification of coefficients in heat equation and wave equation.