A transport problem with semitransparent boundary conditions

The paper deals with a method to study particle transport problems inside a convex domain D with nonhomogeneous boundary conditions which are the result of the evolution of the process outside D. In this way, the existence of a unique classical solution is proved by using the regularity in time of the incoming particle flux. The study is based on some classical results of semigroup theory and the solution of the evolution problem is given by means of the boundary data. Explicit forms of the solution are given also in the case of linear scattering and absorption phenomena, even if there is some given source term on the boundary of D.