On the stability of exact ABCs for the reaction-subdiffusion equation on unbounded domain

TL;DR

This paper derives and analyzes the stability of exact artificial boundary conditions for the reaction-subdiffusion equation on unbounded domains, ensuring well-posedness and long-time stability of the reformulated problem.

Contribution

It introduces exact ABCs for the fractional reaction-subdiffusion equation and proves their stability using Kreiss theory and properties of tempered fractional calculus.

Findings

The exact ABCs effectively truncate the unbounded domain.

The reduced problem is proven to be stable via Kreiss theory.

Long-time stability of the solution is established.

Abstract

In this note we propose the exact artificial boundary conditions formula to the fractional reaction-subdiffusion equation on an unbounded domain. With the application of Laplace transformation, the exact artificial boundary conditions (ABCs) are derived to reformulate the original problem on the unbounded domain to an initial-boundary-value problem on the bounded computational domain. By the Kreiss theory, we prove that the reduced initial-boundary value problem is stability. Based on the properties of tempered fractional calculus, we obtain that the reduced initial-boundary value problem is long-time stability.