  Consider the Cauchy problem of one dimensional porous medium equation (PME)
with reactions. We first prove a general convergence result, that is, any
bounded global solution starting at a nonnegative compactly supported initial
data converges as $t\to \infty$ to a nonnegative zero of the reaction term or a
ground state stationary solution. Based on it, we give out a complete
classification on the asymptotic behaviors of the solutions for PME with
monostable, bistable and combustion types of nonlinearities.
