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Analysis and Optimization of Systems pp 472–483Cite as

Asymptotic behaviour of the solutions to wave equation with nonlinear damping on the boundary

  • Hyperbolic Control Systems
  • Conference paper
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  • 2011 Accesses

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 111))

Abstract

We consider wave equation with the Neumann, nonlinear boundary conditions of the form: ∂y/∂η 1 Γ + γ(y t) ε 0, where γ is a monotone graph. We shall prove that if γ(0)=0, then the corresponding feedback system is strongly stable in the topology of H 1 × L 2. If instead γ(0)ε[−γ0.γ0], then we shall show, that the energy of all limit solutions is uniformly bounded (with respect to initial condition) by a constant C Ω γ0, where C Ω depends on the geometry of the domain Ω, but not on the norm of initial conditions.

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Authors and Affiliations

  1. Department of Applied Mathematics Thomton Hall, University of Virginia, 22903, Chariottesville, VA

    I. Lasiecka

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  1. I. Lasiecka
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A. Bensoussan J. L. Lions

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© 1988 Springer-Verlag

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Lasiecka, I. (1988). Asymptotic behaviour of the solutions to wave equation with nonlinear damping on the boundary. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042237

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  • DOI: https://doi.org/10.1007/BFb0042237

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19237-4

  • Online ISBN: 978-3-540-39161-6

  • eBook Packages: Springer Book Archive

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