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Volume 40, Issue 4
Uniqueness of Transonic Shock Solutions to Euler-Poisson System with Varying Background Charges

Haoran Zheng & Jianqiao Zhang

DOI: 10.4208/cmr.2024-0028

Commun. Math. Res., 40 (2024), pp. 400-412.

Published online: 2024-12

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  • Abstract

In this paper, we investigate a one-dimensional Euler-Poisson system with varying background charges, which are two different constants when the flow speed is less than and greater than the sound speed. Using the shock matching method, we derive the properties of the solution trajectories and establish a monotonic relationship between the density at the nozzle exit and the shock position. This relationship demonstrates the existence and uniqueness of a transonic shock solution under suitable boundary conditions.

  • Keywords

Euler-Poisson system, transonic shock solution, uniqueness, varying background charges.

  • AMS Subject Headings

35B35, 35L67, 35Q81, 76H05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-400, author = {Zheng , Haoran and Zhang , Jianqiao}, title = {Uniqueness of Transonic Shock Solutions to Euler-Poisson System with Varying Background Charges}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {4}, pages = {400--412}, abstract = {

In this paper, we investigate a one-dimensional Euler-Poisson system with varying background charges, which are two different constants when the flow speed is less than and greater than the sound speed. Using the shock matching method, we derive the properties of the solution trajectories and establish a monotonic relationship between the density at the nozzle exit and the shock position. This relationship demonstrates the existence and uniqueness of a transonic shock solution under suitable boundary conditions.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0028}, url = {http://global-sci.org/intro/article_detail/cmr/23699.html} }
TY - JOUR T1 - Uniqueness of Transonic Shock Solutions to Euler-Poisson System with Varying Background Charges AU - Zheng , Haoran AU - Zhang , Jianqiao JO - Communications in Mathematical Research VL - 4 SP - 400 EP - 412 PY - 2024 DA - 2024/12 SN - 40 DO - http://doi.org/10.4208/cmr.2024-0028 UR - https://global-sci.org/intro/article_detail/cmr/23699.html KW - Euler-Poisson system, transonic shock solution, uniqueness, varying background charges. AB -

In this paper, we investigate a one-dimensional Euler-Poisson system with varying background charges, which are two different constants when the flow speed is less than and greater than the sound speed. Using the shock matching method, we derive the properties of the solution trajectories and establish a monotonic relationship between the density at the nozzle exit and the shock position. This relationship demonstrates the existence and uniqueness of a transonic shock solution under suitable boundary conditions.

Zheng , Haoran and Zhang , Jianqiao. (2024). Uniqueness of Transonic Shock Solutions to Euler-Poisson System with Varying Background Charges. Communications in Mathematical Research . 40 (4). 400-412. doi:10.4208/cmr.2024-0028
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