Study of a massless electrons approximation model
 issued from plasma physics and quasineutrality



                        Sylvie Fabre  

              (CMAP - Ecole Polytechnique)



Abstract:  In this paper, we study the existence
 and uniqueness of solutions of Poisson's equation in lRN 
coupled with Boltzmann relation which gives a particular
 expression of the electronic density. We consider also 
the case where the ionic density vanishes. At last, an
 asymptotic analysis yields a proof of the quasineutrality
 hypothesis of this model where the Debye length can be 
neglected in comparison of the size of the system.



Resume  Nous presentons ici une etude de l'existence et 
unicite de solutions de l'equation de Poisson dans lRN co
uplee àa la relation de Boltzmann qui donne une expression p
articuliere de la densite electronique. Le cas d'une densite ion
ique nulle est aussi examine. Enfin, une analyse asymptotique 
permet de prouver la validite de l'hypothese de quasineutralite de
 ce modele oùu la longueur de Debye est negligeable devant la ta
ille du systeme.


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