A particle transport problem with non-homogeneous reflection boundary conditions

We consider particle transport in a three-dimensional convex region V, bounded by the regular surface partial derivative V. We assume that particles are specularly reflected by a partial derivative V and that a source q is assigned on partial derivative V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. (C) 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.