### Abstract

We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach's experiment for the compressible Euler system, i. e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.

Original language | English (US) |
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Pages (from-to) | 177-210 |

Number of pages | 34 |

Journal | Acta Mathematicae Applicatae Sinica |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics