Global existence and asymptotic behavior of solution for the sixth order Boussinesq equation with damped term. (June 2015)

• Record Type: Journal Article
• Authors: Wang, Shubin; Su, Xiao
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 171
• Page End: 185
• Publication Date: 2015-06
• Subjects: Boussinesq equation -- Cauchy problem -- Global existence -- Decay estimates; 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.2015.03.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the small-data Cauchy problem for the sixth order Boussinesq equation with damped term. The decay estimates of solutions to the corresponding linear equation are given by using the dyadic decomposition and some properties of Bessel functions. Then, we prove the global existence and asymptotic of the small amplitude solution in the time-weighted Sobolev space by the contraction mapping principle.