Semigroups for general transport equations with abstract boundary conditions
Résumé
We investigate C_0-semigroup generation properties of the Vlasov equation with general boundary conditions modeled by an abstract boundary operator H. For conservative boundary conditions we show that there is an extension A of the free streaming operator T_H which generates a C_0-semigroup $(V(t))_{t \geq 0}$ in $L^1$. Furthermore, we precisely describe its domain and provide necessary and sufficient conditions ensuring that $(V(t))_{t \geq 0}$ is stochastic.
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