TY - JOUR

T1 - Two-dimensional regular shock reflection for the pressure gradient system of conservation laws

AU - Zheng, Yuxi

N1 - Funding Information:
Focused Research Group, which is a program of the National Science Foundation.

PY - 2006/4

Y1 - 2006/4

N2 - 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.

AB - 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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U2 - 10.1007/s10255-006-0296-5

DO - 10.1007/s10255-006-0296-5

M3 - Article

AN - SCOPUS:33645686459

SN - 0168-9673

VL - 22

SP - 177

EP - 210

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

IS - 2

ER -