Extended Decay Properties for Generalized BBM Equation

Chulkwang Kwak; Claudio Muñoz

doi:10.1007/978-1-4939-9806-7_8

Extended Decay Properties for Generalized BBM Equation

Chulkwang Kwak, Claudio Muñoz

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

3 Scopus citations

Abstract

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 language	English
Title of host publication	Fields Institute Communications
Publisher	Springer
Pages	397-411
Number of pages	15
DOIs	https://doi.org/10.1007/978-1-4939-9806-7_8
State	Published - 2019

Publication series

Name	Fields Institute Communications
Volume	83
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.

Keywords

35Q35
35Q51

Access to Document

10.1007/978-1-4939-9806-7_8

Cite this

@inbook{b6945c800c3947438859e4de89f0fe11,

title = "Extended Decay Properties for Generalized BBM Equation",

abstract = "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.",

keywords = "35Q35, 35Q51",

author = "Chulkwang Kwak and Claudio Mu{\~n}oz",

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: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

doi = "10.1007/978-1-4939-9806-7_8",

language = "English",

series = "Fields Institute Communications",

publisher = "Springer",

pages = "397--411",

booktitle = "Fields Institute Communications",

}

TY - CHAP

T1 - Extended Decay Properties for Generalized BBM Equation

AU - Kwak, Chulkwang

AU - Muñoz, Claudio

N1 - 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.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - 35Q35

KW - 35Q51

UR - http://www.scopus.com/inward/record.url?scp=85075500629&partnerID=8YFLogxK

U2 - 10.1007/978-1-4939-9806-7_8

DO - 10.1007/978-1-4939-9806-7_8

M3 - Chapter

AN - SCOPUS:85075500629

T3 - Fields Institute Communications

SP - 397

EP - 411

BT - Fields Institute Communications

PB - Springer

ER -

Extended Decay Properties for Generalized BBM Equation

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this