Applications of Mathematics, Vol. 66, No. 5, pp. 725-744, 2021


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

Youness Mezzan, Moulay Hicham Tber

Received February 6, 2020.   Published online April 1, 2021.

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.
Keywords:  free boundary problem; sub-optimal boundary control; characteristics method; complementarity constraint; penalization-regularization
Classification MSC:  35R35, 65M25, 49K20, 90C33


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Affiliations:   Youness Mezzan, Moulay Hicham Tber (correspoding author), Cadi Ayyad University, Department of Mathematics, F.S.S., B.P. 2390, Av. Prince Moulay Abdellah, Marrakech 40000, Morocco, e-mail: y.mezzan@uca.ma, hicham.tber@uca.ac.ma


 
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