  In this paper, we are concerned with the large time behavior of viscous shock
wave for the convective porous-media equation with degenerate viscosity. We get
the regularity of the solution for general initial data and prove the shock
wave is nonlinearly stable providing the initial perturbation is small.
Moreover, the $L^\infty$ decay rate is obtained, which generalized the famous
result \cite{osh82}. Note that the traditional energy method and continuity
argument can not be directly used in this paper since the degeneration of
viscosity. One need to fully utilize the sign of perturbation and it
derivatives, decompose the integral domain to ensure that in each domain the
sign is invariant. Then the stability and the decay rate are obtained by energy
method and an area inequality.
