# Global existence and blow-up for space and time nonlocal reaction-diffusion equation

## TL;DR

This paper investigates a fractional reaction-diffusion equation, demonstrating conditions for finite-time blow-up versus global existence, and analyzing the long-term behavior of solutions.

## Contribution

It provides new insights into the conditions leading to blow-up or global solutions for space-time fractional reaction-diffusion equations.

## Key findings

- Solutions can blow up in finite time under certain initial conditions.
- For realistic initial data, solutions exist globally in time.
- The asymptotic behavior of bounded solutions is characterized.

## Abstract

A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.