Exponential decay for a locally damped fifth-order equation posed on the line. (August 2016)

• Record Type: Journal Article
• Authors: Doronin, G.G.; Natali, F.
• Is Part Of: Nonlinear analysis. Volume 30(2016)
• Page Start: 59
• Page End: 72
• Publication Date: 2016-08
• Subjects: Fifth-order equation -- Exponential decay -- Bourgain spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.11.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove the exponential decay of the energy related to a locally damped fifth-order equation posed on the whole real line with the initial datum from a bounded set of L 2 . A local smoothing effect in H 2 is established, which is essential to obtain the necessary a priory estimates. Moreover, it is shown that arguments used in the article can be applied to prove the exponential decay rate of solutions for the Korteweg–de Vries equation with a similar localized damping term provided the initial data are uniformly bounded in L 2 . This last fact improves some previous results.