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Observability for the Wave Equation with Variable Support in the Dirichlet and Neumann Cases

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Informatics in Control, Automation and Robotics (ICINCO 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 613))

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Abstract

We study the observability of the wave equation when the observation set changes over time.

For the one dimensional Neumann problem, using Fourier series, we are able to prove for the exact observability an equivalent condition already known for the Dirichlet problem; see [1].

For the observability problem with Dirichlet boundary conditions, we focus on multidimensional problems and the observability inequality is proven through a multiplier approach.

Besides this, we present some applications and a numerical simulation.

D. Andreucci—Member of Italian G.N.F.M.-I.N.d.A.M.

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References

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Author information

Authors and Affiliations

  1. Mathematics Department, Sapienza University, Piazzale Aldo Moro, 5, 00185, Rome, Italy

    Antonio Agresti

  2. SBAI Department, Sapienza University, Via Antonio Scarpa, 16, 00161, Rome, Italy

    Daniele Andreucci & Paola Loreti

Authors
  1. Antonio Agresti
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  2. Daniele Andreucci
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  3. Paola Loreti
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Corresponding author

Correspondence to Antonio Agresti .

Editor information

Editors and Affiliations

  1. Ford Research and Advanced Engineer, Dearborn, MI, USA

    Oleg Gusikhin

  2. University of Paris-EST Créteil (UPEC), Créteil, France

    Kurosh Madani

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Agresti, A., Andreucci, D., Loreti, P. (2020). Observability for the Wave Equation with Variable Support in the Dirichlet and Neumann Cases. In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics. ICINCO 2018. Lecture Notes in Electrical Engineering, vol 613. Springer, Cham. https://doi.org/10.1007/978-3-030-31993-9_3

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