On nonlinear time-dependent multivelocity transport equations

The aim of this paper is to show the existence and uniqueness of a solution for a class of nonlinear multivelocity neutron transport equations and to present a method for the determination of the solution. A recursion formula for the construction of a solution by the method of successive approximations and an error estimate for approximate solutions are given. Both global and local solutions are discussed. The conditions imposed on the nonlinear equation are directly applicable to the linear multivelocity transport problem, and a recursion formula for this system is also given. In the process of approximations, only successive integrations are involved. This fact indicates a promising possibility for the calculation of numerical results by using a computer. A brief discussion of this possibility and the applicability of the results on nonlinear problems are included.