This paper is concerned with a one-dimensional isentropic compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity, which models the motion of a mixture of two viscous compressible fluids. The case when the pressure $ p(\rho) = \rho^\gamma $, the viscosity $ \nu(\rho, \chi) = \rho^\alpha $, the interface thickness $ \delta(\rho) = \rho^\beta $ and the relaxation time function $ a(\rho, \chi, \chi_y) = \rho^\lambda $ is considered, where $ \rho $ and $ \chi $ are the density and the phase variable, respectively, and $ \gamma, \alpha, \beta, \lambda\in\mathbb{R} $ are parame...
