Asymptotic profile of solutions to the double dispersion equation. (March 2016)

• Record Type: Journal Article
• Authors: Wang, Yu-Zhu; Chen, Si
• Is Part Of: Nonlinear analysis. Volume 134(2016)
• Page Start: 236
• Page End: 254
• Publication Date: 2016-03
• Subjects: 35L30 -- 35B40; Double dispersion equation -- Asymptotic profile -- Decay estimate; 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.2016.01.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we investigate the initial value problem for the double dispersion equation in R n . Decay estimate and asymptotic profile of solutions to the corresponding linear problem are established. The asymptotic profile of solutions to the corresponding linear problem is given by the convolution of the fundamental solutions of heat and free wave equations. Moreover, the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear problem obtained in this paper is optimal under some conditions. Finally, global existence and optimal decay estimate of solutions to the nonlinear problem are also established.