Existence and stability of rarefaction wave to 1-D piston problem for the relativistic full Euler equations

We consider the 1-D piston problem for the compressible relativistic full Euler equations when the total variations of the initial data and the piston velocity are both sufficiently small. By using a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Moreover, we study the asymptotic behavior of the solutions as t→+∞.