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The Benjamin–Bona–Mahony equation with dissipative memory

  • Filippo Dell’OroEmail author
  • Youcef Mammeri
  • Vittorino Pata
Article
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Abstract

We show that the nonlinear contraction semigroup generated by the Benjamin–Bona–Mahony equation with dissipative memory
$$u_{t} - u_{txx} + u_{x} - \int_{0}^{\infty} g(s) u_{xx}(t-s)\, {\rm d}s + u^{p} u_{x} = 0$$
is exponentially stable for every \({p\in\mathbb{N}}\).

Keywords

Benjamin–Bona–Mahony equation Nonlinear contraction semigroup Dissipative memory Exponential stability 

Mathematics Subject Classification

35B35 35B40 35F25 45K05 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Filippo Dell’Oro
    • 1
    Email author
  • Youcef Mammeri
    • 2
  • Vittorino Pata
    • 3
  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrague 1Czech Republic
  2. 2.Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352Université de Picardie Jules VerneAmiensFrance
  3. 3.Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanItaly

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