On pushed wavefronts of monostable equation with unimodal delayed reaction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F21%3AA0000094" target="_blank" >RIV/47813059:19610/21:A0000094 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.aimsciences.org/article/doi/10.3934/dcds.2021103" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/dcds.2021103</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/dcds.2021103" target="_blank" >10.3934/dcds.2021103</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On pushed wavefronts of monostable equation with unimodal delayed reaction

Popis výsledku v původním jazyce

We study the Mackey-Glass type monostable delayed reaction diffusion equation with a unimodal birth function g(u). This model, designed to describe evolution of single species populations, is considered here in the presence of the weak Allee effect (g(u0) &gt; g'(0)u0 for some u0 &gt; 0). We focus our attention on the existence of slow monotonic traveling fronts to the equation: under given assumptions, this problem seems to be rather difficult since the usual positivity and monotonicity arguments are not effective. First, we solve the front existence problem for small delays, h is an element of [0, hp], where hp, given by an explicit formula, is optimal in a certain sense. Then we take a representative piece-wise linear unimodal birth function which makes possible explicit computation of traveling fronts. In this case, we find out that a) increase of delay can destroy asymptotically stable pushed fronts; b) the set of all admissible wavefront speeds has usual structure of a semi-infinite interval [c*, +infinity); c) for each h &gt;= 0, the pushed wavefront is unique (if it exists); d) pushed wave can oscillate slowly around the positive equilibrium for sufficiently large delays.

Název v anglickém jazyce

On pushed wavefronts of monostable equation with unimodal delayed reaction

Popis výsledku anglicky

We study the Mackey-Glass type monostable delayed reaction diffusion equation with a unimodal birth function g(u). This model, designed to describe evolution of single species populations, is considered here in the presence of the weak Allee effect (g(u0) &gt; g'(0)u0 for some u0 &gt; 0). We focus our attention on the existence of slow monotonic traveling fronts to the equation: under given assumptions, this problem seems to be rather difficult since the usual positivity and monotonicity arguments are not effective. First, we solve the front existence problem for small delays, h is an element of [0, hp], where hp, given by an explicit formula, is optimal in a certain sense. Then we take a representative piece-wise linear unimodal birth function which makes possible explicit computation of traveling fronts. In this case, we find out that a) increase of delay can destroy asymptotically stable pushed fronts; b) the set of all admissible wavefront speeds has usual structure of a semi-infinite interval [c*, +infinity); c) for each h &gt;= 0, the pushed wavefront is unique (if it exists); d) pushed wave can oscillate slowly around the positive equilibrium for sufficiently large delays.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Discrete and Continuous Dynamical Systems - Series A

ISSN

1078-0947

e-ISSN

1553-5231

Svazek periodika

41

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

5979-6000

Kód UT WoS článku

000704400800018

EID výsledku v databázi Scopus

2-s2.0-85116591531