Poisson’s equation coupled with Boltzmann’s relation in \(\mathbb{R}^ N\) and quasineutrality. (Étude de l’équation de Poisson couplée à la relation de Boltzmann dans \(\mathbb{R}^ N\) et quasineutralité.) (French) Zbl 0831.76099

Fabre, Sylvie

C. R. Acad. Sci., Paris, Sér. I 320, No. 1, 45-48 (1995).

Summary: We study the existence and uniqueness of solution in \(\mathbb{R}^N\) to Poisson’s equation coupled with Boltzmann’s relation, which gives a particular expression for the electron density. An asymptotic analysis yields a proof of the quasineutrality hypothesis for this model, where the Debye length can be neglected in comparison with the size of the system.

MSC:

76X05	Ionized gas flow in electromagnetic fields; plasmic flow
35Q35	PDEs in connection with fluid mechanics
35Q60	PDEs in connection with optics and electromagnetic theory

Keywords:

existence; uniqueness; electron density; asymptotic analysis; Debye length