Affiliations: Mathématiques Appliquées de Bordeaux, CNRS/Université de Bordeaux I, 351, cours de la Libération, 33405 Talence cedex, France
Note: [] Present address: Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France.
Note: [] Present address: Institut Galilée, LAGA/CNRS, Université de Paris Nord, Avenue J.B. Clément, 93430 Villetaneuse, France.
Note: [] Present address: Laboratoire de Mathématiques Appliquées, CNRS URA 1501, Université Blaise Pascal, 63177 Aubiere Cedex, France.
Abstract: We consider, in the nonsteady‐state case, the problem of emitted charged particles in a plane diode. This problem is described by the Vlasov–Poisson system with singular data converging to some Dirac measures in the velocity space concentrated at t = 0. Under a sufficient condition on the data, which implies that the particles emitted from the cathode are all collected by the anode, we prove that the solutions converge to a measure solution, with support on velocity, of the Vlasov–Poisson system.
