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

In this paper, we prove that the semigroup S(t) generated by the Cauchy problem of the evolution p-Laplacian equation partial derivative u/partial derivative t - div(|del u|(p-2)del u) = 0 (p > 2) is continuous form a weighted L-infinity space to the continuous space C-0(R-N). 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 C-0(R-N). For this purpose, we need to establish the propagation estimates and the space-time decay estimates for the solutions first.