Global attractor for the generalized double dispersion equation. (March 2015)

• Record Type: Journal Article
• Authors: Yang, Zhijian; Feng, Na; Ma, To Fu
• Is Part Of: Nonlinear analysis. Volume 115(2015)
• Page Start: 103
• Page End: 116
• Publication Date: 2015-03
• Subjects: The generalized double dispersion equation -- Elastic waveguide model -- Global weak solutions -- Non-uniqueness -- Supercritical exponent -- Global attractor -- Exponential attractor; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t − Δ u − Δ u t t + Δ 2 u − Δ u t − Δ g ( u ) = f ( x ) . The main result is concerned with nonlinearities g ( u ) with supercritical growth. In that case we construct a subclass G of the limit solutions and show that it has a weak global attractor. Especially, in non-supercritical case, the weak topology becomes strong, the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space.