Study of the Free Streaming Operator in Slab Geometry in Dependence of the Boundary Conditions

We study the free streaming operator T_∧ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the ‘incoming’ and ‘outgoing’ particle fluxes. Under suitable assumptions on the entries of Λ, it is proved that the resolvent operator of T_∧ is positive. It is proved also that T_∧ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T_∧ is improved. © 1997 by B. G. Teubner Stuttgart – John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 717–736 (1997).