ON THE PROPAGATION OF CASCADES IN A MULTILAYER MEDIUM

A cascade of several types of particles propagating in a medium composed of homogeneous layers R/sup lambda / is considered. The boundaries of the layers may be mobile. The particles of the cascade collide with the particles of tae medium, and in the process they are absorbed, scattered, and generate new particles. The functions W/sup lambda / are sought for that give the distribution of particles of each type according to positions and velocities in the assumption that the functions V/sup lambda /, which give the distribution of partlcles in each layer R/sup lambda / it occupied the whole space, are known. For the unknown functions W/sup lambda / there are given an infinite series of integrals that in general show good convergence. The subintegral functions of these integrals are certain products of the functions V/sup lambda /. (tr-auth)