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An instantaneous semi-Lagrangian approach for boundary control of a melting problem

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Abstract

In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples.

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Authors and Affiliations

  1. Department of Mathematics, F.S.S., Cadi Ayyad University, B.P. 2390, Av. Prince Moulay Abdellah, Marrakech, 40000, Morocco

    Youness Mezzan & Moulay Hicham Tber

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  1. Youness Mezzan
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  2. Moulay Hicham Tber
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Correspondence to Moulay Hicham Tber.

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Mezzan, Y., Tber, M.H. An instantaneous semi-Lagrangian approach for boundary control of a melting problem. Appl Math 66, 725–744 (2021). https://doi.org/10.21136/AM.2021.0028-20

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