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 C 0-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 \((V_H (t))_{t \geqslant 0} \) to be stochastic. We apply these results to examples from kinetic theory.
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Arlotti, L., Lods, B. Substochastic semigroups for transport equations with conservative boundary conditions. J. evol. equ. 5, 485–508 (2005). https://doi.org/10.1007/s00028-005-0209-8
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DOI: https://doi.org/10.1007/s00028-005-0209-8