Investigation of the stability of solutions of some inverse problems for transport equations

This thesis consists of four chapters. In the first chapter, some basic definitions and theorems related to the theory of inverse problems are given. In the second chapter, we consider an inverse problem of determination of an absorption coefficient in the free transport equation in a bounded domain. The stability of the solution of the problem is investigated by means of a Carleman estimate which includes two big parameters, (Gaitan and Ouzzane 2013). In the third chapter, we deal with an initial/boundary problem for a transport equation with an integral term and discuss inverse problem of determining a time independent scattering coefficient or total attenuation by boundary data on a suitable sub-boundary. In this context, Lipschitz stability is studied by using a Carleman estimate which is based on a linear weight function and includes one big parameter, (Machida and Yamamoto 2014). In the last section, the stability of the solution of some source and coefficient inverse problems for a transport equation with variable principle part is investigated with the help of a Carleman estimate which is linear with respect to time t and includes one large parameter (Gölgeleyen and Yamamoto 2016).