Global stability of rarefaction wave to the 1-D piston problem for the Compressible Full Euler Equations

In this paper, we study the 1-D piston problem for compressible full Euler equations under the assumptions that the total variation of the initial data and the perturbation of the piston velocity are sufficiently small. By 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 establish the asymptotic behavior of the solutions as t→∞.