Othmane Baiz, Brahim El-Aqqad
Abstract:
In this article we study an inverse parameter identification problem governed
by a nonlinear parabolic equation with a Steklov-type boundary condition,
where the unknown parameter appears simultaneously in the source term,
the boundary nonlinearity, and the initial datum.
We first establish the global well-posedness of the forward problem and prove
the Lipschitz continuity of the solution map with respect to the parameter.
We then formulate the inverse problem as a Tikhonov-regularized minimization problem and
establish existence of regularized solutions, stability with respect to noisy data,
and convergence as the noise level tends to zero, together with an explicit
reconstruction error estimate under a coercivity condition on the
parameter-to-observation map. The theoretical results
are illustrated by numerical experiments on a one-dimensional prototype,
confirming the predicted convergence rates.
Submitted April 4, 2026. Published September 3, 2026.
Math Subject Classifications: 35K20, 35K55, 35R30, 65N20, 65J20.
Key Words: Parabolic equation; Steklov boundary condition; inverse parameter identification;
Lipschitz stability; Tikhonov regularization; Morozov discrepancy principle; parameter-to-observation map.
DOI: 10.58997/ejde.2026.66
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Othmane Baiz Groupe de recherche Analyse Mathématique et Calcul Scientifique (AMSC) FP Ouarzazate, Ibn Zohr University, Morocco email: othman.baiz@gmail.com |
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Brahim El-Aqqad Groupe de recherche Analyse Mathématique et Calcul Scientifique (AMSC) FP Ouarzazate, Ibn Zohr University, Morocco. email: elaqadbrahim@gmail.com |
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