Travelling wave analysis and jump relations for Euler–Poisson model in the quasineutral limit

Article type: Research Article

Authors: Cordier, Stéphane^; | Degond, Pierre | Markowich, Peter | Schmeiser, Christian

Affiliations: CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France | U.F.R. M.I.G., Univ. P. Sabatier, 31062 Toulouse Cedex, France | Techn. Univ., D 1000, Berlin, Germany | Inst. Ang. und Num. Math., A 1040 Wien, Austria

Note: [] Correspondence to: S. Cordier, Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Abstract: This paper is devoted to the travelling wave analysis of the Euler–Poisson model for a plasma consisting of electrons and ions. When the Debye length tends to 0, this system leads to a non-linear hyperbolic system in a non-conservative form called quasineutral Euler system. Our aim is to determine the admissible jump relations and shock solutions for the quasineutral Euler system as limits of travelling wave solutions for the Euler–Poisson system. We show that only one of the three types of travelling wave solutions converges to admissible shock solutions of the quasineutral Euler system.

DOI: 10.3233/ASY-1995-11301

Journal: Asymptotic Analysis, vol. 11, no. 3, pp. 209-240, 1995