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

Youness MezzanMoulay Hicham Tber — 2021

Applications of Mathematics

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...

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