Methods and Applications of Analysis

Volume 28 (2021)

Number 3

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part II

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Hsiao’s PDE theory on semi-conductor and plasma and their applications

Pages: 249 – 264

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n3.a1

Authors

Yue-Hong Feng (School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China)

Xin Li (School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China)

Shu Wang (School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China)

Abstract

Appreciating of the contributions on PDE of Professor Ling Hsiao, we review Hsiao’s PDE theory on semiconductor and plasma and their applications. As an example of application of Hsiao’s PDE theory on semiconductor and plasma, we study the asymptotic regimes of the compressible Euler–Maxwell equations on plasma. The derivation of the one fluid non-isentropic Euler–Maxwell system from the two-fluid model in terms of the asymptotic expansion method is performed, and the mathematical analysis of the stability of both constant equilibrium solutions and non-constant equilibrium solutions is given on $\mathbb{T}^3$ or $\mathbb{R}^3$.

Keywords

Hsiao’s PDE theory on semiconductor and plasma, drift-diffusion equations, Euler–Maxwell equations, small parameter limits, stability

2010 Mathematics Subject Classification

35B40, 35Q35, 35Q60

Full Text (PDF format)

The authors are supported by the the BNSF (1164010, 1132006), NSFC (11771031, 11531010, 11831003), NSF of Qinghai Province (2017-ZJ-908), NSF of Henan Province (162300410084), the Key Research Fund of Henan Province (16A110019), the general project of scientific research project of the Beijing education committee of China (KM202111232008), and the research fund of Beijing Information Science and Technology University (2025029).

Received 17 July 2020

Accepted 20 January 2021

Published 10 June 2022