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Networks and Heterogeneous Media

2007, Volume 2, Issue 3: 425-479. doi: 10.3934/nhm.2007.2.425
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Stabilization of the wave equation on 1-d networks with a delay term in the nodal feedbacks

  • 1.
    Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, F-59313 - Valenciennes Cedex 9
  • Received: 01 October 2006 Revised: 01 May 2007

  • Primary: 35L05, 93D15; Secondary: 35L10.

  • In this paper we consider the wave equation on 1-d networks with a delay term in the boundary and/or transmission conditions. We first show the well posedness of the problem and the decay of an appropriate energy. We give a necessary and sufficient condition that guarantees the decay to zero of the energy. We further give sufficient conditions that lead to exponential or polynomial stability of the solution. Some examples are also given.

    Citation: Serge Nicaise, Julie Valein. Stabilization of the wave equation on 1-d networks with a delay term in the nodal feedbacks[J]. Networks and Heterogeneous Media, 2007, 2(3): 425-479. doi: 10.3934/nhm.2007.2.425

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