GLOBAL EXISTENCE, ASYMPTOTICS AND UNIQUENESS FOR THE REFLECTION KERNEL OF THE ANGULARLY SHIFTED TRANSPORT-EQUATION

A nonlinear integrodifferential initial value problem, which is induce d from a ''simple transport model,'' is investigated. The underlying e quation contains two parameters c and alpha. Here c (c greater than or equal to O) denotes the fraction of the scattering per collision and alpha (O less than or equal to alpha less than or equal to 1) is an an gular shift. In this paper, we exploit the relationship between the so lution in the half space and that in slab geometry. We are thus able t o show that the problem has a unique, positive, uniformly bounded and globally defined solution for O less than or equal to c less than or e qual to 1 and O less than or equal to alpha less than or equal to 1. M oreover, it is shown that such global solution converges to the minima l positive solution of the half space problem as the spatial variable approaches infinity (i.e. the slab becomes thicker).