Generalized solution of non-autonomous photon transport problem

The purpose of this paper is to show the existence of a generalized solution of a non-autonomous transport problem. By means of the theory of equicontinuous evolution system on a sequentially complete locally convex topological vector space, we show that the perturbed abstract non-autonomous Cauchy problem has a unique solution when the perturbation operator and forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the non-autonomous photon transport problem.