Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Abstract

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

Keywords

• fractional diffusion
• generalized self-similar solution
• blow-up
• global existence
• uniqueness