Zeitschrift für angewandte Mathematik und Physik

, Volume 59, Issue 2, pp 244–263

Global existence of shock front solutions in 1-dimensional piston problem in the relativistic Euler equations

Article

DOI: 10.1007/s00033-007-5121-3

Cite this article as:
Xu, Y. & Dou, Y. Z. angew. Math. Phys. (2008) 59: 244. doi:10.1007/s00033-007-5121-3

Abstract.

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.

Mathematics Subject Classification (2000).

35L5035L6535L6776Y05

Keywords.

Piston problemrelativistic Euler equationsshock front solutionGlimm schemeinteraction of waves

Copyright information

© Birkhaeuser 2007

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina