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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.

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