Carleman estimates for transport equations and applications

This thesis consists of three sections. The first section is devoted to some essential definitions and theorems. In the second section definition of the Carleman estimate for a second order differential operator is given and a Carleman estimate for a nonstationary transport equation is derived. Simple heat equation, direct derivation of a Carleman estimate for a parabolic equation and a global Carleman estimate are introduced. Finally, in the third section stabilities of some inverse problems for transport equations which are used in modelling of propagation of light in biological tissues or in atmosphere and neutrons in reactors etc. are investigated as applications of Carleman estimates.