Some Unexplored Topics in The Reconstruction of Scalar Parameters of Subdiffusion

TL;DR

This paper explores the numerical reconstruction of scalar parameters in fractional diffusion equations with nonlocal terms, addressing gaps in understanding inverse problems with limited temporal data.

Contribution

It investigates the numerical aspects of reconstructing parameters in nonlocal fractional diffusion models, focusing on challenges with short-time observations.

Findings

Addresses open questions on numerical reconstruction with small time data

Highlights the impact of nonlocal terms on inverse problem analysis

Provides insights into the stability and feasibility of parameter recovery

Abstract

In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models. Although, under suitable assumptions on the data, inverse problems associated with recovery of these parameters are nowadays well understood, several important questions related with numerical reconstructions of these parameters via a nonlocal observation in a small time interval have not yet been analyzed. This paper aims to provide some answers.