Two-dimensional regular shock reflection for the pressure gradient system of conservation laws

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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 languageEnglish (US)
Pages (from-to)177-210
Number of pages34
JournalActa Mathematicae Applicatae Sinica
Volume22
Issue number2
DOIs
Publication statusPublished - Apr 1 2006

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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