BLOW-UP FOR A FULLY FRACTIONAL HEAT EQUATION

We study the existence and behaviour of blowing-up solutions to the fully fractional heat equation Mu = u(p), x is an element of R-N, 0< t < Twith p > 0, where M is a nonlocal operator given by a space-time kernel M(x, t) = cN ,at- N2 -1-ae- (|x|2/)4t 1{t>0}, 0 < sigma < 1. This operator coincides with the fractional power of the heat operator, M = (partial derivative t-Delta)a defined through semigroup theory. We characterize the global existence exponent p0 = 1 and the Fujita exponent p* =1+ 2 sigma/ N+2(1-sigma) . We also study the rate at which the blowing-up solutions below p* tend to infinity, IIu(<middle dot>, t)II infinity similar to(T - t) sigma p-1 .