Acta Mathematicae Applicatae Sinica

, Volume 22, Issue 2, pp 177–210 | Cite as

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

Original Papers

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.

Keywords

Free boundary oblique derivative tangential oblique derivative 2-D Riemann problem regular reflection Mach reflection gas dynamics 

2000 MR Subject Classification

35L65 35J70 35R35 35J65 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity Park, PA 16802

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