Example of supersonic solutions to a steady state Euler-Poisson system

Yue-Jun Peng (1) , Ingrid Violet (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We give an example of supersonic solutions to a one-dimensional steady state Euler-Poisson system arising in the modeling of plasmas and semiconductors. The existence of the supersonic solutions which correspond to large current density is proved by Schauder's fixed point theorem. We show also the uniqueness of solutions in the supersonic region.

Mots clés: Euler-Poisson equations; Steady state flow; Supersonic solutions; Existence; Uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

Yue-Jun Peng, Ingrid Violet. Example of supersonic solutions to a steady state Euler-Poisson system. Applied Mathematics Letters, 2006, 19 (12), pp.1335-1340. ⟨hal-00489009⟩