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DUAN Ben

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Academic Titles:
Gender:Male
Alma Mater:The Chinese University of Hong Kong
Degree:Doctoral Degree
Status:On the job
School/Department:School of Mathematics, Dalian University of Technology
Discipline:Applied Mathematics
Business Address:Office: Room1135, Innovation Park Building, DLUT
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Current position: Home >> Scientific Research >> Paper Publications

TRANSONIC SHOCK SOLUTIONS TO THE EULER-POISSON SYSTEM IN QUASI-ONE-DIMENSIONAL NOZZLES

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Indexed by:Journal Papers

First Author:Duan, Ben

Correspondence Author:Xiao, JJ (reprint author), Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China.

Co-authors:Luo, Zhen,Xiao, Jingjing

Date of Publication:2016-01-01

Journal:COMMUNICATIONS IN MATHEMATICAL SCIENCES

Included Journals:SCIE

Volume:14

Issue:4

Page Number:1023-1047

ISSN No.:1539-6746

Key Words:Euler-Poisson system; transonic shock; dynamic stability

Abstract:In this paper, we study the transonic shock solutions to the Euler-Poisson system in quasi-one-dimensional nozzles. For a given supersonic flow at the entrance of the nozzle, under some proper assumptions on the data and nozzle length we first obtain a class of steady transonic shock solutions for the exit pressure lying in a suitable range. The shock position is monotonically determined by the exit pressure. More importantly, by the estimates on the coupled effects of the electric field and the geometry of the nozzle, we prove the dynamic stability of the transonic shock solutions under suitable physical conditions. As a consequence, there indeed exist dynamically stable transonic shock solutions for the Euler-Poisson system in convergent nozzles, which is not true for the Euler system.