On sentinel method of one-phase Stefan problem

Authors

  • Merabti Nesrine Lamya Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria
  • Iqbal M. Batiha 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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Published

2023-11-08

How to Cite

On sentinel method of one-phase Stefan problem. (2023). Journal of the Nigerian Society of Physical Sciences, 5(4), 1772. https://doi.org/10.46481/jnsps.2023.1772

Issue

Volume 5, Issue 4, November 2023

Section

Original Research
Copyright & Licensing

Copyright (c) 2023 Merabti Nesrine Lamya, Iqbal M. Batiha, Imad Rezzoug, Adel Ouannas, Taki-Eddine Ouassaeif

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On sentinel method of one-phase Stefan problem. (2023). Journal of the Nigerian Society of Physical Sciences, 5(4), 1772. https://doi.org/10.46481/jnsps.2023.1772