Continuity of solution of inverse problems for the equation of radiation transfer

The theory of inverse problems for the particle transport equation is one of the rapidly developing areas of modern mathematics. This article discusses the continuity of the solution of inverse problems for the radiative transfer equation in multi-zone regions from $R$. In fact, the inverse problem is studied for the non-stationary radiative transfer equation, which consists in simultaneously finding the scattering coefficient $\sigma_s$ and radiation intensity $u$. In this case, it suffices to prove the continuity of the solution of the inverse problem from $R$ with respect to additional information. In this paper, we study the local properties of the classical solution of the single speed time-dependent equation considered in a multi-zone domain.