DYNAMICS OF GLOBAL ATTRACTOR FOR A SEMILINEAR DEGENERATE PARABOLIC EQUATION INVOLVING GRUSHIN OPERATORS

TitleDYNAMICS OF GLOBAL ATTRACTOR FOR A SEMILINEAR DEGENERATE PARABOLIC EQUATION INVOLVING GRUSHIN OPERATORS
Publication TypeJournal Article
Year of Publication2018
AuthorsLEE JIHOON
JournalDynamic Systems and Applications
Volume27
Issue3
Start Page457
Pagination18
Date Published2018
ISSN1056-2176
AMS Subject Classification35B05, 35J70
Abstract

In this paper we study the dynamics of global attractor of a semilinear parabolic equation involving Grushin operators. First we show that the global attractor is bounded in ${ L^∞(Ω) }$ and ${ D(A) }$. Then we investigate the existence of a Lyapunov function, the injectivity on the global attractor and the squeezing property. Finally, we obtain estimates on upper bound and lower bound of the fractal dimension of the global attractor.

PDFhttps://acadsol.eu/dsa/articles/27/3/2.pdf
DOI10.12732/dsa.v27i3.2
Refereed DesignationRefereed
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