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Finite-Time Stabilization and Impulse Control of Heat Equation with Dynamic Boundary Conditions

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Abstract

In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is impulse null controllable at any positive time via impulse controls supported in a nonempty open subset of the physical domain. Furthermore, we infer an explicit estimate for the exponential decay of the solution. The proof of the main result combines a logarithmic convexity estimate and some spectral properties associated to dynamic boundary conditions. In our setting, the nature of the equations, which couple intern-boundary phenomena, makes it necessary to go into quite sophisticated estimates incorporating several boundary terms.

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Authors and Affiliations

  1. LMDP, UMMISCO (IRD-UPMC), Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, Morocco

    Salah-Eddine Chorfi, Ghita El Guermai , Lahcen Maniar & Walid Zouhair

Authors
  1. Salah-Eddine Chorfi
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  2. Ghita El Guermai
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  3. Lahcen Maniar
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  4. Walid Zouhair
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Correspondence to Walid Zouhair.

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Chorfi, SE., El Guermai , G., Maniar, L. et al. Finite-Time Stabilization and Impulse Control of Heat Equation with Dynamic Boundary Conditions. J Dyn Control Syst 29, 1585–1615 (2023). https://doi.org/10.1007/s10883-023-09646-0

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  • DOI: https://doi.org/10.1007/s10883-023-09646-0

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