@Article{CSIAM-AM-4-1,
author = {Duan, Ben and Zhen, Luo and Yuanyuan, Xing},
title = {Radial Transonic Shock Solutions to Euler-Poisson System with Varying Background Charge in an Annulus},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {1},
pages = {129--156},
abstract = {<p style="text-align: justify;">This paper concerns both the structural and dynamical stabilities of radially
symmetric transonic shock solutions for two-dimensional Euler-Poisson system in an
annulus. The density of fixed, positively charged background ions is allowed to be different constants in supersonic and subsonic regimes. First, the existence and structural
stability of a steady transonic shock solution are obtained by the monotonicity between
the shock location and the density on the outer circle. Second, any radially symmetric
transonic shock solution with respect to small perturbations of the initial data is shown
to be dynamically stable. The proof relies on the decay estimates and coupled effects
from electric field and geometry of the annulus, together with the methods from [18].
These results generalize previous stability results on transonic shock solutions for constant background charge.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0007},
url = {https://global-sci.com/article/82284/radial-transonic-shock-solutions-to-euler-poisson-system-with-varying-background-charge-in-an-annulus}
}