Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹
Chaosheng Zhu
Annales Polonici Mathematici, Tome 113 (2015), p. 219-234 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:280894 
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     author = {Chaosheng Zhu},
     title = {Attractor of a semi-discrete Benjamin-Bona-Mahony equation on $\mathbb{R}$$^1$},
     journal = {Annales Polonici Mathematici},
     volume = {113},
     year = {2015},
     pages = {219-234},
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     language = {en},
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Chaosheng Zhu. Attractor of a semi-discrete Benjamin-Bona-Mahony equation on ℝ¹. Annales Polonici Mathematici, Tome 113 (2015) pp. 219-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-2/