Self-similar solutions of the p-Laplace heat equation: the case when p > 2

We, study the self-similar solutions of the equation ut - div (vertical bar del u vertical bar(p-2)del u) = 0, in R-N, when p > 2. We make a complete study of the existence and possible uniqueness of solutions of the form u(x,t) = (+/-t)(-alpha/beta)omega((+/-t)(-1 beta)vertical bar x vertical bar) of any sign, regular or singular at x = 0. Among them we find solutions with all expanding Compact support or a shrinking hole (for t > 0), or a spreading compact support a focusing hole (for t < 0). When t < 0, we show the existence of positive solutions oscillating around the particular Solution U(x,t) = C-N,C-p(vertical bar x vertical bar(p)/(-t)(1/(p-2)).