A PARTICLE-TRANSPORT PROBLEM WITH NONHOMOGENEOUS 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 p articles are specularly reflected by a partial derivative V and that a source q is assigned on partial derivative V; more general non-homoge neous boundary conditions are also discussed. The problem is non-linea r because the boundary condition is not homogeneous. We prove existenc e 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 bou ndary source q. In the appendix, we indicate how some properties of af fine operators can be used to derive the solution. (C) 1998 B. G. Teub ner Stuttgart-John Wiley & Sons, Ltd.