Identifying a space-dependent source term in distributed order time-fractional diffusion equations

Dinh Nguyen Duy Hai

doi:10.3934/mcrf.2022025

Article Contents

2023, Volume 13, Issue 3: 1008-1022. Doi: 10.3934/mcrf.2022025

This issue Previous Article Barrier Lyapunov functions-based adaptive neural tracking control for non-strict feedback stochastic nonlinear systems with full-state constraints: A command filter approach Next Article Impulse null approximate controllability for heat equation with dynamic boundary conditions

Identifying a space-dependent source term in distributed order time-fractional diffusion equations

Dinh Nguyen Duy Hai

Department of Economic Mathematics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

Received: February 2022

Revised: April 2022

Early access: November 2022

Published: September 2023

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Abstract

The aim of this paper is to investigate an inverse problem of recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such a problem is ill-posed and has important practical applications. For this problem, we propose a general regularization method based on the idea of the filter method. With a suitable source condition, we prove that the method is of optimal order under various choices of regularization parameter. One is based on the a priori regularization parameter choice rule and another one is the discrepancy principle. Finally, the capabilities of our method are illustrated by both the Tikhonov and the Landweber method.

Keywords:

Inverse source problem,
distributed order time-fractional diffusion equation,
ill-posed problem,
regularization,
order optimal error estimate.

Mathematics Subject Classification: Primary: 26A33, 35R30, 47A52; Secondary: 65N15.

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