Remark on the Cauchy problem for the evolution p-Laplacian equation

In this paper, we prove that the semigroup [Formula: see text] generated by the Cauchy problem of the evolution p-Laplacian equation [Formula: see text] ([Formula: see text]) is continuous form a weighted [Formula: see text] space to the continuous space [Formula: see text]. Then we use this property to reveal the fact that the evolution p-Laplacian equation generates a chaotic dynamical system on some compact subsets of [Formula: see text]. For this purpose, we need to establish the propagation estimates and the space-time decay estimates for the solutions first.