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

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Assume a single reaction-diffusion equation has zero as an asymptotically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim inf(vertical bar x vertical bar -> infinity) u(x), lim sup(vertical bar x vertical bar -> infinity) 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.
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2013-08
Language
English
Article Type
Article
Keywords

POSITIVE SOLUTIONS; UNIQUENESS; RN; EXISTENCE; SYMMETRY

Citation

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.33, no.8, pp.3707 - 3718

ISSN
1078-0947
DOI
10.3934/dcds.2013.33.3707
URI
http://hdl.handle.net/10203/173576
Appears in Collection
MA-Journal Papers(저널논문)
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