Study of a massless electrons approximation modelissued

In this paper, we study the existence and uniqueness in I R N of Poisson's equation coupled with Boltzmann's relation which gives a particular expression of the electron's 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 with the size of the system. R esum e-Cet article etudie l'existence et l'unicit e de la solution de l' equation de Poisson dans I R N coupl ee a la relation de Boltzmann qui donne une expression particuli ere de la densit e electronique. Le cas d'une densit e ionique nulle est examin e. Ennn, une analyse asymptotique permet de prouver la validit e de l'hypoth ese de quasineutralit e de ce mod ele o u la longueur de Debye est n egligeable devant la taille du syst eme.