We consider the free streaming operator associated with conservative boundary conditions. It is known that this operator (with its usual domain) admits an extension A which generates a strongly continuous semigroup V(t). With techniques borrowed from the additive perturbation theory of substochasic semigroups, we describe precisely the domain of A and provide necessary and sufficient conditions ensuring V(t) to be stochastic. We apply these results to examples from kinetic theory.
Substochastic semigroups for transport equations with conservative boundary conditions
ARLOTTI, Luisa;
2005-01-01
Abstract
We consider the free streaming operator associated with conservative boundary conditions. It is known that this operator (with its usual domain) admits an extension A which generates a strongly continuous semigroup V(t). With techniques borrowed from the additive perturbation theory of substochasic semigroups, we describe precisely the domain of A and provide necessary and sufficient conditions ensuring V(t) to be stochastic. We apply these results to examples from kinetic theory.File in questo prodotto:
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