Extended Decay Properties for Generalized BBM Equation

Chulkwang Kwak, Claudio Muñoz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations


In this note we show that all small solutions of the BBM equation must decay to zero as t → +∞ in large portions of the physical space, extending previous known results, and only assuming data in the energy space. Our results also include decay on the left portion of the physical line, unlike the standard KdV dynamics.

Original languageEnglish
Title of host publicationFields Institute Communications
Number of pages15
StatePublished - 2019

Publication series

NameFields Institute Communications
ISSN (Print)1069-5265
ISSN (Electronic)2194-1564

Bibliographical note

Funding Information:
We thank F. Rousset and M. A. Alejo for many interesting discussions on this subject and the BBM equation. C. K. is supported by FONDECYT Postdoctorado 2017 Proyect N?3170067. C. M. work was partly funded by Chilean research grants FONDECYT1150202, Fondo Basal CMM-Chile, MathAmSud EEQUADD and Millennium Nucleus Center for Analysis of PDE NC130017. Part of this work was carried out while the authors were part of the Focus Program on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (August 2017) held at Fields Institute, Canada. They would like to thank the Institute and the organizers for their warming support.

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.


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