Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space

Abstract

The system of equations describing motion of compressible viscoelastic fluids is considered in a one dimensional half space under the outflow boundary condition. We investigate the existence and stability of stationary solutions. It is shown that the stationary solution exists for large Mach number and small number of propagation speed of elastic wave. We next show that the stationary solution is asymptotically stable, provided that the initial perturbation is sufficiently small.

Keywords

• compressible viscoelastic system
• energy method
• outflow problem
• stationary solution
• asymptotic stability