APPROXIMATIONS OF EULER-MAXWELL SYSTEMS BY DRIFT-DIFFUSION EQUATIONS THROUGH ZERO-RELAXATION LIMITS NEAR NON-CONSTANT EQUILIBRIUM

作     者：Jin, Rui Li, Yachun Zhao, Liang 

作者机构：School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences CMA-Shanghai MOE-LSC SHL-MAC Shanghai Jiao Tong University Shanghai200240 China Mathematical Modelling & Data Analytics Center Oxford Suzhou Centre for Advanced Research Suzhou215123 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Maxwell equations 

摘      要：Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the zero-relaxation limit towards the drift-diffusion equations with non-constant doping functions. We carry out the global-in-time convergence analysis by establishing uniform estimates of solutions near non-constant equilibrium regarding the relaxation parameter and passing to the limit by using classical compactness arguments. Furthermore, stream function methods are carefully generalized to the non-constant equilibrium case, with which as well as the anti-symmetric structure of the error system and an induction argument, we establish global-in-time error estimates between smooth solutions to the Euler-Maxwell system and those to drift-diffusion system, which are bounded by some power of relaxation *** Codes 35B25, 35L45, 35Q60, 35K45 Copyright © 2023, The Authors. All rights reserved.