Asymptotic Stability of the Rarefaction Wave for the Non-Viscous and Heat-Conductive Ideal Gas in Half Space

This article is concerned with the impermeable wall problem for an ideal poly-tropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof is given by an elementary energy method and the key point is to do the higher order derivative estimates with respect to tbecause of the less dissipativity of the system and the higher order derivative boundary terms.