Benjamin–Bona–Mahony Equations with Memory and Rayleigh Friction

Benjamin–Bona–Mahony Equations with Memory and Rayleigh Friction

This paper is concerned with the integrodifferential Benjamin-Bona-Mahony equation u t - u txx + α u - ∫ 0 ∞ g ( s ) u xx ( t - s ) d s + ( 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...

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Veröffentlicht in:Applied mathematics & optimization 2021-04, Vol.83 (2), p.813-831
Hauptverfasser: Dell’Oro, Filippo, Mammeri, Youcef
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Fractal geometry
Fractals
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Systems Theory
Theoretical
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Mammeri, Youcef
description This paper is concerned with the integrodifferential Benjamin-Bona-Mahony equation u t - u txx + α u - ∫ 0 ∞ g ( s ) u xx ( t - s ) d s + ( 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.
doi_str_mv 10.1007/s00245-019-09568-z
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subjects Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Fractal geometry
Fractals
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Systems Theory
Theoretical
title Benjamin–Bona–Mahony Equations with Memory and Rayleigh Friction
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