On the Blow-Up of Solutions for a Fractional Diffusion Equation with Nonlinear Memory and Reaction Terms in a Bounded Domain

In this paper, we present sharp blow-up and global existence results for a fractional diffusion equation with nonlinear memory and reaction terms in a bounded domain, where the fractional derivative in time is taken in the sense of Caputo type. Our proof relies on comparison techniques and on a variant of the eigenfunction method combined with the asymptotic behavior of the solution of a fractional differential inequality. Moreover, a new method is developed for proving blow-up results in the critical case.