Global existence of shock front solutions in 1-dimensional piston problem in the relativistic Euler equations
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- Xu, Y. & Dou, Y. Z. angew. Math. Phys. (2008) 59: 244. doi:10.1007/s00033-007-5121-3
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The paper studies the 1-D piston problem of the relativistic Euler equations when the speed of the piston is a perturbation of a constant. A sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to the weak solution (which includes a strong leading shock) to the piston problem. In particular, we give the precise estimates on the reflection of the perturbed waves on the piston and the leading shock.