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 equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.
Conservation Laws Preprint Server <conservation@math.ntnu.no> 2005-02-15 13:36:49 UTC