Benjamin–Bona–Mahony Equations with Memory and Rayleigh Friction

  • Filippo Dell’OroEmail author
  • Youcef Mammeri


This paper is concerned with the integrodifferential Benjamin-Bona-Mahony equation
$$\begin{aligned} u_t - u_{txx} + \alpha u - \int _0^\infty g(s) u_{xx}(t-s) \mathrm{d}s + (f(u))_x = h \end{aligned}$$
complemented with Dirichlet boundary conditions, in the presence of a possibly large external force h. The nonlinearity f is allowed to exhibit a superquadratic growth, and the dissipation is due to the simultaneous interaction between the nonlocal memory term and the Rayleigh friction. The existence of regular global and exponential attractors of finite fractal dimension is shown.


Benjamin–Bona–Mahony equation Dissipative memory Rayleigh friction Exponential attractors 

Mathematics Subject Classification

35B41 35F25 45K05 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Laboratoire Amiénois de Mathématique Fondamentale et AppliquéeCNRS UMR 7352, Université de Picardie Jules Verne80039France
  3. 3.Institut de Génétique, Environnement et Protection des PlantesINRA UMR 134935650France

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