Classical solutions to a mixed-type PDE with a Keldysh-type degeneracy and accelerating transonic solutions to the Euler-Poisson system
Analysis of PDEs
2025-05-23 v1
Abstract
In this paper, we first prove the existence of classical solutions to a class of Keldysh-type equations. Next, we apply this existence result to prove the structural stability of one-dimensional smooth transonic solutions to the steady Euler-Poisson system. Most importantly, the solutions constructed in this paper are classical solutions to the Euler-Poisson system, thus their sonic interfaces are not weak discontinuities in the sense that all the flow variables, such as density, velocity and pressure, are at least across the interfaces.
Cite
@article{arxiv.2505.16354,
title = {Classical solutions to a mixed-type PDE with a Keldysh-type degeneracy and accelerating transonic solutions to the Euler-Poisson system},
author = {Myoungjean Bae and Ben Duan and Chunjing Xie},
journal= {arXiv preprint arXiv:2505.16354},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2308.04694