Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

Chenyu Zhang (), Fan Yang and Xiaoxiao Li
Additional contact information
Chenyu Zhang: School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Fan Yang: School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Xiaoxiao Li: School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Mathematics, 2024, vol. 12, issue 2, 1-28

Abstract: In this paper, we delve into the challenge of identifying an unknown source in a space-time fractional diffusion-wave equation. Through an analysis of the exact solution, it becomes evident that the problem is ill-posed. To address this, we employ both the Tikhonov regularization method and the Quasi-boundary regularization method, aiming to restore the stability of the solution. By adhering to both a priori and a posteriori regularization parameter choice rules, we derive error estimates that quantify the discrepancies between the regularization solutions and the exact solution. Finally, we present numerical examples to illustrate the effectiveness and stability of the proposed methods.

Keywords: space-time fractional diffusion-wave equation; Tikhonov regularization method; quasi-boundary regularization method; ill-posed problem; identifying the unknown source (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/231/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/231/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:2:p:231-:d:1316788

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().