On the Stability of Contact Discontinuity for the <scp>1D</scp> Compressible Full Navier‐Stokes‐Allen‐Cahn System With Free Boundary

ABSTRACT This paper is concerned with the large‐time behavior of solutions to the one‐dimensional full compressible Navier‐Stokes‐Allen‐Cahn system with a free boundary. The model can be used to describe the motion of a mixture of two viscous compressible fluids. We first construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation. Then we prove that the viscous contact wave is time‐asymptotically stable, provided that the strength of contact wave and the initial perturbation are sufficiently small. The proof is given by the elementary ‐energy method.