Slowly oscillating wavefronts of the KPP-Fisher delayed equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F14%3A%230000451" target="_blank" >RIV/47813059:19610/14:#0000451 - isvavai.cz</a>
Result on the web
<a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9762" target="_blank" >http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9762</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2014.34.3511" target="_blank" >10.3934/dcds.2014.34.3511</a>
Alternative languages
Result language
angličtina
Original language name
Slowly oscillating wavefronts of the KPP-Fisher delayed equation
Original language description
This paper concerns the semi-wavefronts (i.e. bounded solutions u = phi(x.v+ct) >0, |v| = 1, satisfying phi(-infinity) = 0) to the delayed KPP-Fisher equation u(t)(t, x) = x) u(t, x)(1-u(t -tau,x)), u >= 0, x is an element of R-m First, we show that theprofile phi of each semi-wavefront should be either monotone or eventually sine-like slowly oscillating around the positive equilibrium. Then a solution to the problem of existence of semi-wavefronts is provided. Next, we prove that the semi-wavefronts are in fact wavefronts (i.e. additionally phi(+infinity) = 1) if c >= 2 and tau <= 1; our proof uses dynamical properties of an auxiliary one-dimensional map with the negative Schwarzian. However, we also show that, for c >= 2 and tau >= 1.87, each semi-wavefront profile phi(t) should develop non-decaying oscillations around 1 as t ->+infinity.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/EE2.3.20.0002" target="_blank" >EE2.3.20.0002: Development of Research Capacities of the Mathematical Institute in Opava</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems
ISSN
1078-0947
e-ISSN
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Volume of the periodical
34
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
3511-3533
UT code for WoS article
000333556300012
EID of the result in the Scopus database
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