Acta Mathematicae Applicatae Sinica

, Volume 22, Issue 2, pp 177–210

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

Original Papers

DOI: 10.1007/s10255-006-0296-5

Cite this article as:
Zheng, Y. Acta Mathematicae Applicatae Sinica, English Series (2006) 22: 177. doi:10.1007/s10255-006-0296-5


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.


Free boundaryoblique derivativetangential oblique derivative2-D Riemann problemregular reflectionMach reflectiongas dynamics

2000 MR Subject Classification


Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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