STUDY OF THE FREE STREAMING OPERATOR IN SLAB GEOMETRY IN DEPENDENCE OF THE BOUNDARY-CONDITIONS

We study the free streaming operator T-Lambda, in a slab domain with b oundary conditions described by a linear matrix operator Lambda acting between the 'incoming' and 'outgoing' particle fluxes. Under suitable assumptions on the entries of Lambda, it is proved that the resolvent operator of T-Lambda is positive. It is proved also that T Lambda is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Lambda. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T-Lambda is improved. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.