Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

Abstract

We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $\mathbb{R}_{+}\times \mathbb{R}^N$. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.

Keywords

• coupled fractional-diffusion equations
• polynomial nonlinearities
• global solution
• blow-up