BLOW-UP RATES FOR A FRACTIONAL HEAT EQUATION

We study the speed at which nonglobal solutions to the fractional heat equation ut |(-Delta) (alpha/2)u = u(p), with 0 < alpha < 2 and p > 1, tend to infinity. We prove that, assuming either p < p(F) equivalent to 1 + alpha/N or u is strictly increasing in time, then for t close to the blow-up time T it holds that parallel to u(center dot, t)parallel to infinity similar to (T - t)(-1/p-1). The proofs use elementary tools, such as rescaling or comparison arguments.

Automated summary

The study focuses on the speed of convergence to infinity of nonglobal solutions to the fractional heat equation ut |(-Delta) (alpha/2)u = u(p). It is proven that under certain conditions, the behavior of the solution near the blow-up time can be characterized. Elementary tools such as rescaling or comparison arguments are used in the proofs.