Existence and uniqueness of a soluton to the nonstationary transport equation

We consider the problem of finding the flux density of particles whose transport process is described by a nonstationary integro-differential equation. We study the case that the medium in which the process takes place is inhomogeneous; in other words, the coefficients of the equation may have jumps of the first kind. The initial data is the density of the intput flux and the density at the initial time moment. A solution to the problem is understood in the weak sense. It is shown that a solution exists, is unique, and can be represented as a uniformly convergent series.