Asymptotic stability of strong contact discontinuity for full compressible Navier-Stokes equations with initial boundary value problem

This paper is concerned with Dirichlet problem $u(0,t)=0$, $\theta (0,t)={\theta }_{-}$ for one-dimensional full compressible Navier-Stokes equations in the half space ${\mathbb{R}}_{+}=(0,+\mathrm{\infty })$. Because the boundary decay rate is hard to control, stability of contact discontinuity result is very difficult. In this paper, we raise the decay rate and establish that for a certain class of large perturbation, the asymptotic stability result is contact discontinuity. Also, we ask the strength of contact discontinuity not small. The proofs are given by the elementary energy method.