Abstract transport equations with divergence free force field


We investigate C0-semigroup generation properties of the Vlasov equation with general boundary conditions modeled by an abstract boundary operator H . For multiplicative boundary conditions we adapt techniques from [17] and in the case of conservative boundary conditions we show that there is an extension A of the free streaming operator TH which generates a C0semigroup (VH(t))t>0 in L. Furthermore, following the ideas of [5], we precisely describe its domain and provide necessary and sufficient conditions ensuring that (VH(t))t>0 is stochastic. CONTENTS

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@inproceedings{Arlotti2007AbstractTE, title={Abstract transport equations with divergence free force field}, author={Luisa Arlotti and Jacek Banasiak and Bertrand Lods}, year={2007} }