Regularity of the solution to fractional diffusion, advection, reaction equations in weighted Sobolev spaces

In this article we investigate the regularity of the solution to the fractional diffusion, advection, reaction equation on a bounded domain in R-1. The analysis is performed in the weighted Sobolev spaces, H-(a,b)(s) (I) Three different characterizations of H-(a,b)(s)(I) are presented, together with needed embedding theorems for these spaces. The analysis shows that the regularity of the solution is bounded by the endpoint behavior of the solution, which is determined by the parameters alpha and r defining the fractional diffusion operator. Additionally, the analysis shows that for a sufficiently smooth right hand side function, the regularity of the solution to fractional diffusion reaction equation is lower than that of the fractional diffusion equation. Also, the regularity of the solution to fractional diffusion advection reaction equation is two orders lower than that of the fractional diffusion reaction equation. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This article investigates the regularity of solutions to the fractional diffusion, advection, reaction equation on a bounded domain in R-1. The regularity of the solution is determined by the endpoint behavior of the solution, and it is lower for a sufficiently smooth right hand side function. The regularity of the solution to the fractional diffusion advection reaction equation is two orders lower than that of the fractional diffusion reaction equation.