On sentinel method of one-phase Stefan problem

Merabti Nesrine  Lamya; Iqbal M. Batiha; Imad  Rezzoug; Adel  Ouannas; Taki-Eddine  Ouassaeif

doi:10.46481/jnsps.2023.1772

Authors

Merabti Nesrine Lamya Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria
Iqbal M. Batiha
[email protected]
Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan | Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE
Imad Rezzoug Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria
Adel Ouannas Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria
Taki-Eddine Ouassaeif Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria

Keywords:

Sentinel method, Approximate controllability, Stefan’s problem

Abstract

This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated.

Dimensions

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