Asymptotic stability of rarefaction wave and boundary layer for outflow problem on the viscous vasculogenesis model *

In this paper, we are concerned with the outflow problem on a simplified viscous vasculogenesis model in the half-line . Firstly, we establish the global-in-time asymptotic stability of the rarefaction wave. Secondly, we obtain the unique existence and decay property of the boundary layer by using stable manifold theorem. Moreover, the asymptotic stability and convergence rates of solution towards boundary layer are obtained. The appearance of concentration makes the stationary problem more difficult than Navier–Stokes equations or Navier–Stokes–Poisson equations.