Exterior Problem of the Linear Vlasov–Poisson–Boltzmann System

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1792-1823
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume51
Issue number3
Online published7 May 2019
Publication statusPublished - 2019

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Abstract

We will present in this paper a linear theory on a flow under the effect of a self-induced electric field past an obstacle governed by the Vlasov-Poisson-Boltzmann equation. The bulk velocity at infinity acts like a driving force on the flow so that some nontrivial stationary solution profile exists. Similar to Ukai and Asano's work on the exterior problem for the Boltzmann equation, the spectrum of the linear operator is used through an approach in the spirit of the limiting absorption in scattering theory. However, to take care of the electric potential that satisfies the coupled Poisson equation, a new decomposition of the solution operator is needed to show the compactness.

Research Area(s)

  • Vlasov-Poisson-Boltzmann system, exterior problem, stationary solution, spectrum analysis, BOUNDARY-VALUE-PROBLEM, GLOBAL EXISTENCE, STEADY SOLUTIONS, EQUATION, OBSTACLE

Citation Format(s)

Exterior Problem of the Linear Vlasov–Poisson–Boltzmann System. / DONG, Hongjie; YANG, Tong; ZHONG, Mingying.
In: SIAM Journal on Mathematical Analysis, Vol. 51, No. 3, 2019, p. 1792-1823.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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