Strong Global Attractors for 3D Wave Equations with Weakly Damping. (13th June 2012)

• Record Type: Journal Article
• Authors: Meng, Fengjuan
• Other Names: Lai Shaoyong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-06-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/469382
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider the existence of the global attractor A 1 for the 3D weakly damped wave equation. We prove that A 1 is compact in ( H 2 ( Ω ) ∩ H 0 1 ( Ω ) ) × H 0 1 ( Ω ) and attracts all bounded subsets of ( H 2 ( Ω ) ∩ H 0 1 ( Ω ) ) × H 0 1 ( Ω ) with respect to the norm of ( H 2 ( Ω ) ∩ H 0 1 ( Ω ) ) × H 0 1 ( Ω ) . Furthermore, this attractor coincides with the global attractor in the weak energy space H 0 1 ( Ω ) × L 2 ( Ω ) .