Slowly oscillating wavefronts of the KPP-Fisher delayed equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Slowly oscillating wavefronts of the KPP-Fisher delayed equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Slowly oscillating wavefronts of the KPP-Fisher delayed equation

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.20.0002" target="_blank" >EE2.3.20.0002: Rozvoj vědeckých kapacit Matematického ústavu Slezské univerzity v Opavě</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete and Continuous Dynamical Systems

ISSN

1078-0947

e-ISSN

—

Svazek periodika

34

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

3511-3533

Kód UT WoS článku

000333556300012

EID výsledku v databázi Scopus

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