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Exponential Stability of the Wave Equation with Memory and Time Delay

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New Prospects in Direct, Inverse and Control Problems for Evolution Equations

Part of the book series: Springer INdAM Series ((SINDAMS,volume 10))

Abstract

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough.

In memory of Alfredo Lorenzi

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Author information

Authors and Affiliations

  1. LMAM, Université de Lorraine and CNRS (UMR 7122), 57045, Metz Cedex 1, France

    Fatiha Alabau-Boussouira

  2. LAMAV FR CNRS 2956, Institut des Sciences et Techniques de Valenciennes, Université de Valenciennes et du Hainaut Cambrésis, 59313, Valenciennes Cedex 9, France

    Serge Nicaise

  3. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, 67010, L’Aquila, Italy

    Cristina Pignotti

Authors
  1. Fatiha Alabau-Boussouira
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  2. Serge Nicaise
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  3. Cristina Pignotti
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Corresponding author

Correspondence to Cristina Pignotti .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Bologna, Milano, Italy

    Angelo Favini

  2. Dipartimento di Matematica, Università di Bari, Bari, Bari, Italy

    Genni Fragnelli

  3. Dipartimento di Matematica, Università di Bari, Bari, Bari, Italy

    Rosa Maria Mininni

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Alabau-Boussouira, F., Nicaise, S., Pignotti, C. (2014). Exponential Stability of the Wave Equation with Memory and Time Delay. In: Favini, A., Fragnelli, G., Mininni, R. (eds) New Prospects in Direct, Inverse and Control Problems for Evolution Equations. Springer INdAM Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-11406-4_1

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