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

Convergence of Solutions of the Porous Medium Equation with Reactions