Global Lipschitz stability in determining coefficients of the radiative transport equation

Abstract

In this paper, for the radiative transport equation, we study inverse problems of determining a time-independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making a one time input of a pair of a positive initial value and boundary data on a suitable sub-boundary. The main results are Lipschitz stability estimates. We can also prove the reverse inequalities, which means that our estimates for the inverse problems are the best possible. The proof is based on a Carleman estimate with a linear weight function.