A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data

Ray Abney, Thuy T. Le, Loc H. Nguyen and Cam Peters

Applied Mathematics and Computation, 2025, vol. 494, issue C

Abstract: We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the “reduced dimensional method.” Initially, we use the polynomial-exponential basis to approximate the inverse problem as a system of 1D nonlinear equations. We then employ a Picard iteration based on the quasi-reversibility method and a Carleman weight function. We will rigorously prove that the sequence derived from this iteration converges to the accurate solution for that 1D system without requesting a good initial guess of the true solution. The key tool for the proof is a Carleman estimate. We will also show some numerical examples.

Keywords: Time reduction; Carleman Picard iteration; Nonlinear; Parabolic (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032500013X
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:494:y:2025:i:c:s009630032500013x

DOI: 10.1016/j.amc.2025.129286

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().