English

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 C1C^1 across the interfaces.

Keywords

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