Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 8
71
Views
0
CrossRef citations to date
0
Altmetric
Articles

Lipschitz stability in inverse source problems for a singular parabolic equation

, &
Pages 2805-2824 | Received 24 Apr 2017, Accepted 03 Sep 2020, Published online: 01 Oct 2020
 

ABSTRACT

In this paper, we study inverse source problems for the heat equation with an inverse-square potential localized on the boundary of a smooth bounded domain, and with a locally distributed observation. We first derive an improved Carleman estimate of that obtained by Cazacu [SIAM J Control Optim. 2014;52:2055–2089] and then use it to prove the Lipschitz stability result for the inverse source problem.

COMMUNICATED BY:

2010 Mathematics Subject Classifications:

Acknowledgements

The authors would like to thank the reviewers for their helpful comments and suggestions which improved the presentation of the paper. This work was completed while the first and second authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). They would like to thank the Institute for its hospitality and support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.