Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations

Yong Jung Kim; Wei Ming Ni; Masaharu Taniguchi

doi:10.3934/dcds.2013.33.3707

Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations

Yong Jung Kim, Wei Ming Ni, Masaharu Taniguchi

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Assume a single reaction-diüsion equation has zero as an asymp- totically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim infjxj!1 u(x); lim supjxj!1 u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.

Original language	English (US)
Pages (from-to)	3707-3718
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	8
DOIs	https://doi.org/10.3934/dcds.2013.33.3707
State	Published - Aug 2013

Keywords

Reaction-diüsion equations
Travelling spots
Travelling waves

Publisher link

10.3934/dcds.2013.33.3707

Find It

Find It at U of M Libraries

Cite this

@article{57794a71a5be4e62a57228e6433bbf32,

title = "Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations",

abstract = "Assume a single reaction-di{\"u}sion equation has zero as an asymp- totically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim infjxj!1 u(x); lim supjxj!1 u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.",

keywords = "Reaction-di{\"u}sion equations, Travelling spots, Travelling waves",

author = "Kim, {Yong Jung} and Ni, {Wei Ming} and Masaharu Taniguchi",

year = "2013",

month = aug,

doi = "10.3934/dcds.2013.33.3707",

language = "English (US)",

volume = "33",

pages = "3707--3718",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "8",

}

TY - JOUR

T1 - Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations

AU - Kim, Yong Jung

AU - Ni, Wei Ming

AU - Taniguchi, Masaharu

PY - 2013/8

Y1 - 2013/8

N2 - Assume a single reaction-diüsion equation has zero as an asymp- totically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim infjxj!1 u(x); lim supjxj!1 u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.

AB - Assume a single reaction-diüsion equation has zero as an asymp- totically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim infjxj!1 u(x); lim supjxj!1 u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.

KW - Reaction-diüsion equations

KW - Travelling spots

KW - Travelling waves

UR - http://www.scopus.com/inward/record.url?scp=84872970954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872970954&partnerID=8YFLogxK

U2 - 10.3934/dcds.2013.33.3707

DO - 10.3934/dcds.2013.33.3707

M3 - Article

AN - SCOPUS:84872970954

SN - 1078-0947

VL - 33

SP - 3707

EP - 3718

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 8

ER -

Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this