STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

doi:10.1007/s10473-024-0416-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1487-1506.doi: 10.1007/s10473-024-0416-4

STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

Yang Cao¹, Yuanyuan Xing^1,*, Na Zhang²

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. School of mathematics and statistics, Wuhan University, Wuhan 430070, China

收稿日期:2023-04-13 出版日期:2024-08-25 发布日期:2024-08-30

STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

Yang Cao¹, Yuanyuan Xing^1,*, Na Zhang²

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. School of mathematics and statistics, Wuhan University, Wuhan 430070, China

Received:2023-04-13 Online:2024-08-25 Published:2024-08-30
Contact: *E-mail: yxing_math@163.com
About author:E-mail: mathcy@163.com;nzhang@whu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (11871134, 12171166) and the Fundamental Research Funds for the Central Universities (DUT23LAB303).

摘要/Abstract

摘要： This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length. The background charge in the Poisson equation is a piecewise constant function. The structural stability of the steady transonic shock solution is obtained by the monotonicity argument. Furthermore, this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data. One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.

关键词: Euler-Poisson system, transonic shock, varying background charges, stability

Abstract: This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length. The background charge in the Poisson equation is a piecewise constant function. The structural stability of the steady transonic shock solution is obtained by the monotonicity argument. Furthermore, this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data. One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.

Key words: Euler-Poisson system, transonic shock, varying background charges, stability

中图分类号:

35B35

Yang Cao, Yuanyuan Xing, Na Zhang. STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES[J]. 数学物理学报(英文版), 2024, 44(4): 1487-1506.

Yang Cao, Yuanyuan Xing, Na Zhang. STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1487-1506.

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STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

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