A new solution representation for the BBM equation in a quarter plane and the eventual periodicity

John Meng Kai Hong, Jiahong Wu, Juan Ming Yuan

Research output: Contribution to journalArticlepeer-review

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Abstract

The initial-boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behaviour (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. Towards this end, we derive a new formula representing solutions of this initial- and boundary-value problem by inverting the operator ∂t+α∂x - γ∂xxt defined in the space-time quarter plane. The eventual periodicity of the linearized BBM equation with periodic boundary data and forcing term is established by combining this new representation formula and the method of stationary phase. The eventual periodicity of the full BBM equation is obtained under a suitable assumption imposed on its solution.

Original languageEnglish
Pages (from-to)1927-1944
Number of pages18
JournalNonlinearity
Volume22
Issue number8
DOIs
StatePublished - 2009

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