We describe the asymptotic behaviour of the exact controls and the corresponding states of the wave equation in a ε- periodic two component composite with a jump of the solution on the interface depending on a parameter γ. The approach to the exact controllability process is developed by applying the Hilbert Uniqueness Method, introduced by J. -L. Lions. We prove that, according to the values of γ, the exact controls and the corresponding solutions of the ε-problems converge to the exact controls of different homogenized problems and to the corresponding solutions, respectively.
Recent results on the exact controllability of problems with imperfect interface
Monsurrò, Sara
2023
Abstract
We describe the asymptotic behaviour of the exact controls and the corresponding states of the wave equation in a ε- periodic two component composite with a jump of the solution on the interface depending on a parameter γ. The approach to the exact controllability process is developed by applying the Hilbert Uniqueness Method, introduced by J. -L. Lions. We prove that, according to the values of γ, the exact controls and the corresponding solutions of the ε-problems converge to the exact controls of different homogenized problems and to the corresponding solutions, respectively.File in questo prodotto:
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