Abstract: We studied the obstruction phenomenon aris ing from the solution of the evolution p-Laplaceequation with p∈(1,2)∪(2,+∞). The L^∞-obstruction phenomenon in the case of p>2(slow diffusion) and the L¹-obstruction phenomenon in the case of 1<p<2 (fast diffusion) were proved respectively. For the slow diffusion equation with the source term, we also obtained the finite propagation property of solution.

Key words: obstruction phenomenon, finite propagation, degeneracy, singularity