Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹

• Autorzy: Chaosheng Zhu
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the study of the large time behavior and especially the regularity of the global attractor for the semi-discrete in time Crank-Nicolson scheme to discretize the Benjamin-Bona-Mahony equation on ℝ¹. Firstly, we prove that this semi-discrete equation provides a discrete infinite-dimensional dynamical system in H¹(ℝ¹). Then we prove that this system possesses a global attractor $𝓐_τ$ in H¹(ℝ¹). In addition, we show that the global attractor $𝓐_τ$ is regular, i.e., $𝓐_τ$ is actually included, bounded and compact in H²(ℝ¹). Finally, we estimate the finite fractal dimensions of $𝓐_τ$.

Kategorie tematyczne

• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 35B45: A priori estimates
• 35B41: Attractors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 115
• Numer: 3
• Strony: 219-234

Daty

wydano

2015

Twórcy

autor

Chaosheng Zhu

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, P.R. China

Identyfikatory

DOI

10.4064/ap115-3-2