Upper semicontinuity of global attractors for a family of semilinear wave equations with gentle dissipation. (July 2017)

• Record Type: Journal Article
• Authors: Yang, Zhijian; Liu, Zhiming
• Is Part Of: Applied mathematics letters. Volume 69(2017:Jul.)
• Page Start: 22
• Page End: 28
• Publication Date: 2017-07
• Subjects: Upper semicontinuity -- Semilinear wave equations -- Gentle dissipation -- Global attractor; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.01.006
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The paper investigates the upper semicontinuity of global attractors A α of a family of semilinear wave equations with gentle dissipation: u t t − △ u + γ ( − △ ) α u t + f ( u ) = g ( x ), with α ∈ ( 0, 1 ∕ 2 ) . It is a continuation of researches in Yang et al. (2016), where the existence of global attractors of the equations has been established. We further show that for any neighborhood U of A α 0, α 0 ∈ ( 0, 1 ∕ 2 ), A α ⊂ U when 0 < α − α 0 ≪ 1 .