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. |