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Indirect Boundary Controllability of Coupled Degenerate Wave Equations

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Abstract

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.

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Authors and Affiliations

  1. FST Errachidia, MAIS Laboratory, MAMCS Group, Moulay Ismail University of Meknes, P.O. Box 509, Boutalamine, 52000, Errachidia, Morocco

    Alhabib Moumni, Jawad Salhi & Mouhcine Tilioua

Authors
  1. Alhabib Moumni
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  2. Jawad Salhi
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  3. Mouhcine Tilioua
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All authors contributed equally to this work.

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Correspondence to Jawad Salhi.

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Moumni, A., Salhi, J. & Tilioua, M. Indirect Boundary Controllability of Coupled Degenerate Wave Equations. Acta Appl Math 190, 12 (2024). https://doi.org/10.1007/s10440-024-00649-y

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