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.
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Partially supported by NSF-DMS-0305497 and 0305114.
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Zheng, Y. Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws. Acta Mathematicae Applicatae Sinica, English Series 22, 177–210 (2006). https://doi.org/10.1007/s10255-006-0296-5
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DOI: https://doi.org/10.1007/s10255-006-0296-5
Keywords
- Free boundary
- oblique derivative
- tangential oblique derivative
- 2-D Riemann problem
- regular reflection
- Mach reflection
- gas dynamics