On time-dependent and stationary solutions to the linear Boltzmann equation

This article considers the linear time-dependent Boltzmann equation in a bounded domain with general reflecting boundary conditions, together with an interior source term and an absorption term, both these terms with time-dependent coefficient going to zero, when time goes to infinity. First, mild L-1-solutions are constructed as limits of iterate functions. Then the problem of convergence to a stationary solution is studied by an H-theorem, using a relative entropy functional.