Theory and iterative solution of a model for fission-product deposition

This paper presents a study of an initial boundary value problem for a certain (semi-linear) hyperbolic system of two partial differential equations. This problem is a dimensionless form of a mathematical model which occurred in the study of fission product deposition in gas-cooled nuclear reactors. The problem is shown to have a unique solution. It is further proved that the solution satisfies physically reasonable bounds and approaches a solution of the corresponding steady state problem as $t \to \infty $ . An iterative approximation scheme is shown to converge to the solution and to give alternating upper and lower bounds on the solution. Numerical results show that this iterative scheme should have practical merit for a certain parametric range.