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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
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:494:y:2025:i:c:s009630032500013x

DOI: 10.1016/j.amc.2025.129286

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