Regularized solutions for an inverse problem governed by a parabolic Steklov equation

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.

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BibTeX RIS

BibTeX

@article{baiz2026regularized,
  title = {{Regularized solutions for an inverse problem governed by a parabolic Steklov equation}},
  author = {Othmane Baiz and Brahim El-Aqqad},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = sep,
  url = {http://ejde.math.txstate.edu/Volumes/2026/66/abstr.html},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Regularized solutions for an inverse problem governed by a parabolic Steklov equation
AU  - Othmane Baiz
AU  - Brahim El-Aqqad
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/66/abstr.html
AB  - 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.
SN  - 1072-6691
ER  -

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