Attractors for the Generalized Benjamin–Bona–Mahony Equation

Abstract

We consider the periodic initial-boundary value problem for a multidimensional generalized Benjamin Bona Mahony equation. We show the existence of the global attractor with a finite fractal dimension and the existence of the exponential attractor for the corresponding semigroup. Academic Press

Asymptotic smoothing and attractors for the generalized Benjamin–Bona–Mahony equation onR3

“…The decay rates of solutions were investigated in [3][4][5]13,34,50] and the references therein. When the equation is defined in a bounded domain, the existence and finite dimensionality of the global attractor were proved in [6,16,46,49]. The regularity of the global attractor was established in [47] when the forcing term g ∈ H k with k 0, and the Gevrey regularity was proved in [18] when g is in a Gevrey class.…”

Persistence of bounded solutions to degenerate Sobolev-Galpern equations

“…Regard (3) as the form (NH), where X = L 2 (0, π), M = I − ζΔ, L 0 = −kΔ and B(t) ≡ 0. In [7] the operator M is degenerate. In particular, for N = 1 and ζ = −1/n 2 , associated with the boundary condition u(0, t) = u(π, t) = 0, the equation satisfies N (M ) = span{sin nx}.…”

“…in [7,8,20,23]. Regard (3) as the form (NH), where X = L 2 (0, π), M = I − ζΔ, L 0 = −kΔ and B(t) ≡ 0.…”

Numerical study of the Benjamin-Bona-Mahony-Burgers equation

“…In recent years, many different methods have been used to estimate the solution of the Benjamin-Bona-Mahony-Burgers equation and the BBM equation, for example, see [3,4,5,7,11]. The paper is organized as follows.…”