The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation

Abstract

In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions. We next provide sufficient conditions for the existence of global solutions by using the results of Zhang and Sun. In conclusion, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

Keywords

• time-fractional diffusion equation
• blow-up
• global existence
• critical exponent