Stability and $ L^{p}$ convergence rates of planar diffusion waves for three-dimensional bipolar Euler-Poisson systems

Yeping Li; Jie Liao

doi:10.3934/cpaa.2019062

Article Contents

2019, Volume 18, Issue 3: 1281-1302. Doi: 10.3934/cpaa.2019062

This issue Previous Article Ground states of nonlinear Schrödinger systems with periodic or non-periodic potentials Next Article Solvability of nonlocal systems related to peridynamics

Stability and $ L^{p}$ convergence rates of planar diffusion waves for three-dimensional bipolar Euler-Poisson systems

Yeping Li and
Jie Liao^,

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

* Corresponding author: Jie Liao
* Corresponding author: Jie Liao

Received: May 2018

Revised: August 2018

Published: May 2019

The research is partially supported by NSFC grants 11671134 and 11871335.

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Abstract

In the paper, we consider a three-dimensional bipolar hydrodynamic model from semiconductor devices and plasmas. This system takes the form of Euler-Poisson with electric field and relaxation term added to the momentum equations. We first construct the planar diffusion waves. Next we show the global existence of smooth solutions for the initial value problem of three-dimensional bipolar Euler-Poisson systems when the initial data are near the planar diffusive waves. Finally, we also establish the $ L^p(p∈[2,+∞])$ convergence rates of the solutions toward the planar diffusion waves. A frequency decomposition, approximate Green function and delicate energy method are used to prove our results.

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Mathematics Subject Classification: 35M20, 35Q35, 76W05.

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