Open AccessStrong Global Attractors for 3D Wave Equations with Weakly Damping
Author(s) -
Fengjuan Meng
Publication year - 2012
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2012/469382
Subject(s) - attractor , mathematics , bounded function , norm (philosophy) , wave equation , mathematical analysis , space (punctuation) , pure mathematics , linguistics , philosophy , political science , law
We consider the existence of the global attractor A1 for the 3D weakly damped wave equation. We prove that A1 is compact in (H2(Ω)∩H01(Ω))×H01(Ω) and attracts all bounded subsets of (H2(Ω)∩H01(Ω))×H01(Ω) with respect to the norm of (H2(Ω)∩H01(Ω))×H01(Ω). Furthermore, this attractor coincides with the global attractor in the weak energy space H01(Ω)×L2(Ω)
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