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An instantaneous semi-Lagrangian approach for boundary control of a melting problem
Applications of Mathematics, Tome 66 (2021) no. 5, pp. 725-744 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2021.0028-20
Classification : 35R35, 49K20, 65M25, 90C33
Keywords: free boundary problem; sub-optimal boundary control; characteristics method; complementarity constraint; penalization-regularization 
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     title = {An instantaneous {semi-Lagrangian} approach for boundary control of a melting problem},
     journal = {Applications of Mathematics},
     pages = {725--744},
     year = {2021},
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Mezzan, Youness; Tber, Moulay Hicham. An instantaneous semi-Lagrangian approach for boundary control of a melting problem. Applications of Mathematics, Tome 66 (2021) no. 5, pp. 725-744. doi: 10.21136/AM.2021.0028-20

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