Initial-boundary value problems for coupled systems of time-fractional diffusion equations

TL;DR

This paper studies initial-boundary value problems for coupled time-fractional diffusion equations, establishing existence, uniqueness, and asymptotic behavior, and addresses an inverse problem for determining fractional orders from partial observations.

Contribution

It introduces a framework for coupled fractional diffusion systems, proving key properties and solving an inverse problem unique to such coupled dynamics.

Findings

Unique existence of solutions established

Long-time asymptotic behavior characterized

Inverse problem for fractional orders solved

Abstract

This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior of the solution, which mostly inherit those of a single equation. Owing to the coupling effect, we also obtain the uniqueness for an inverse problem on determining all the fractional orders by the single point observation of a single component of the solution.