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Shock Diffraction Problem by Convex Cornered Wedges for Isothermal Gas

Authors
  • Wang, Qin1
  • Song, Kyungwoo2
  • 1 Yunnan University, Kunming, 650091, China , Kunming (China)
  • 2 Kyung Hee University, Seoul, 02447, Korea , Seoul (South Korea)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 01, 2021
Volume
41
Issue
4
Pages
1130–1140
Identifiers
DOI: 10.1007/s10473-021-0407-7
Source
Springer Nature
Keywords
License
Yellow

Abstract

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establish the global existence of solutions and prove the C012\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C^{0,{1 \over 2}}}$$\end{document}-regularity of solutions near the degenerate boundary. We also compare the difference of solutions between the isothermal gas and the polytropic gas.

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