# zbMATH — the first resource for mathematics

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
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