Plenary talk
Blow-up for a fully fractional equation
We study the existence and behaviour of blowing-up solutions to the fully fractional heat equation \begin{equation} \mathcal M u = u^p, \qquad x \in \mathbb R^d, 0 < t < T \end{equation} with $p > 1$, where $\mathcal M$ is a nonlocal operator given by a space-time kernel $M (x,t) = c_{N,\sigma}t^{-\frac N 2- 1- \sigma} e^{-\frac{|x|^2}{4t}} 1_{t>0}$, $0 < \sigma < 1$, an example of a master equation. This operator coincides with the fractional operator $\mathcal M = (\partial_t - \Delta)^\sigma$ defined through semigroup theory. We characterize the global existence exponent and the Fujita exponente, and study the rate at which the blowing-up solution tends to infinity.