Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system. (English) Zbl 1227.35070

Li, Yeping

Discrete Contin. Dyn. Syst., Ser. B 16, No. 1, 345-360 (2011).

A two- and three-dimensional bipolar Euler-Poisson system (hydrodynamic model) is studied. The system arises in mathematical modeling for semiconductors and plasmas. The steady state isentropic case supplemented by the proper boundary conditions is considered. First the author shows the existence and uniqueness of irrotational subsonic stationary solutions for the two- and three-dimensional hydrodynamic model. Next, he investigates the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit for above stationary solutions, respectively. For each limit, it is shown the strong convergence of the sequence of solutions and one gives the associated convergence rates.

Reviewer: Titus Petrila (Cluj-Napoca)

MSC:

35B40	Asymptotic behavior of solutions to PDEs
35Q31	Euler equations
82D10	Statistical mechanics of plasmas
35Q60	PDEs in connection with optics and electromagnetic theory
35B25	Singular perturbations in context of PDEs

Keywords:

zero-electron-mass limit; zero-relaxation-time limit; quasi-neutral limit; irrotational subsonic stationary solutions; two-dimensional model; three-dimensional model