Structural stability of Supersonic solutions to the Euler-Poisson system
Abstract
The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into a second order hyperbolic-elliptic coupled system together with several transport equations. One of the key ingredients of the analysis is to obtain the well-posedness of the boundary value problem for the associated linearized hyperbolic-elliptic coupled system, which is achieved via a delicate choice of multiplier to gain energy estimate. The nonlinear structural stability of supersonic solution in the general situation is established by combining the iteration method with the estimate for hyperbolic-elliptic system and the transport equations together.
Cite
@article{arxiv.1602.01892,
title = {Structural stability of Supersonic solutions to the Euler-Poisson system},
author = {Myoungjean Bae and Ben Duan and Jingjing Xiao and Chunjing Xie},
journal= {arXiv preprint arXiv:1602.01892},
year = {2019}
}
Comments
The paper was revised substantially in this new version. In particular, we constructed the new multiplier under general conditions on the background solutions