A Blow-up Dichotomy for Semilinear Fractional Heat Equations

Abstract

We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.

19 pages

References in corpus (1)

• Well-posedness of the Cauchy problem for the fractional power dissipative equations

Cited by in corpus (1)

• Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces