This paper is concerned with the integrodifferential Benjamin-Bona-Mahony equation ut-utxx+αu-∫0∞g(s)uxx(t-s)ds+(f(u))x=h 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 Equations with Memory and Rayleigh Friction

Dell'Oro F.;
2021-01-01

Abstract

This paper is concerned with the integrodifferential Benjamin-Bona-Mahony equation ut-utxx+αu-∫0∞g(s)uxx(t-s)ds+(f(u))x=h 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.
2021
Benjamin–Bona–Mahony equation
Dissipative memory
Exponential attractors
Rayleigh friction
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1167252
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