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 C0-semigroup (V_H (t))_{t \geqslant 0} in L^1. With techniques borrowed from the additive perturbation theory of substochastic semigroups, we describe precisely its domain and provide necessary and sufficient conditions ensuring (V_H (t))_t to be stochastic. We apply these results to examples from kinetic theory.
Substochastic semigroups for transport equations with conservative boundary conditions
LODS, BERTRAND
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 C0-semigroup (V_H (t))_{t \geqslant 0} in L^1. With techniques borrowed from the additive perturbation theory of substochastic semigroups, we describe precisely its domain and provide necessary and sufficient conditions ensuring (V_H (t))_t to be stochastic. We apply these results to examples from kinetic theory.
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