Asymptotic analysis of the transient Vlasov–Poisson system for a plane diode

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.