UN PROBLEMA TRIDIMENSIONALE DI TRASPORTO FUORI DI UNA SFERA RIFLETTENTE

Abstract

In this paper we study the linear monoenergetic Boltzmann equation in the space
external to a sphere ofradius n> f} with specular refiectionboundary conditions- By means oftheory
of linear positive operator semigroups in Banach spaces we Show that streaming operator is the
infinitesimal generator ofa strongly continuous; semigroup of positive contractions. of which we
give the explicit form, and that Boltzmann ope rator is the infinitesimal generator of an irreducible
Strongly continuous semigroup- Moreover we study completely the spectrum of streaming
operator,