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

Chaosheng Zhu. "Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹." Annales Polonici Mathematici 115.3 (2015): 219-234. <http://eudml.org/doc/280894>.

@article{ChaoshengZhu2015,
abstract = {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 $_τ$ in H¹(ℝ¹). In addition, we show that the global attractor $_τ$ is regular, i.e., $_τ$ is actually included, bounded and compact in H²(ℝ¹). Finally, we estimate the finite fractal dimensions of $_τ$.},
author = {Chaosheng Zhu},
journal = {Annales Polonici Mathematici},
keywords = {Crank-Nicolson scheme; regularity; fractal dimension},
language = {eng},
number = {3},
pages = {219-234},
title = {Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹},
url = {http://eudml.org/doc/280894},
volume = {115},
year = {2015},
}

TY - JOUR
AU - Chaosheng Zhu
TI - Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹
JO - Annales Polonici Mathematici
PY - 2015
VL - 115
IS - 3
SP - 219
EP - 234
AB - 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 $_τ$ in H¹(ℝ¹). In addition, we show that the global attractor $_τ$ is regular, i.e., $_τ$ is actually included, bounded and compact in H²(ℝ¹). Finally, we estimate the finite fractal dimensions of $_τ$.
LA - eng
KW - Crank-Nicolson scheme; regularity; fractal dimension
UR - http://eudml.org/doc/280894
ER -