About: Slowly oscillating wavefronts of the KPP-Fisher delayed equation

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9762
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 the profile 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. 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 the profile 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. (en)
Title	Slowly oscillating wavefronts of the KPP-Fisher delayed equation Slowly oscillating wavefronts of the KPP-Fisher delayed equation (en)
skos:prefLabel	Slowly oscillating wavefronts of the KPP-Fisher delayed equation Slowly oscillating wavefronts of the KPP-Fisher delayed equation (en)
skos:notation	RIV/47813059:19610/14:#0000451!RIV15-MSM-19610___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(EE2.3.20.0002)
http://linked.open...iv/cisloPeriodika	9
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Hasík, Karel Trofimchuk, Sergei
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	45353
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/14:#0000451
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Upper and lower solutions; monotone traveling waves; slowly oscillating fronts; Wright's equation (en)
http://linked.open.../riv/klicoveSlovo	Upper and lower solutions Wright's equation monotone traveling waves slowly oscillating fronts
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[145E88A262DB]
http://linked.open...i/riv/nazevZdroje	Discrete and Continuous Dynamical Systems
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Development of Research Capacities of the Mathematical Institute in Opava
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	34
http://linked.open...iv/tvurceVysledku	Hasík, Karel Trofimchuk, Sergei
http://linked.open...ain/vavai/riv/wos	000333556300012
issn	1078-0947
number of pages	23 (xsd:int)
http://bibframe.org/vocab/doi	10.3934/dcds.2014.34.3511
http://localhost/t...ganizacniJednotka	19610

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