Traveling waves in the nonlocal KPP-Fisher equation: Different roles of the right and the left interactions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3AN0000159" target="_blank" >RIV/47813059:19610/16:N0000159 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0022039615007007" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022039615007007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2015.12.035" target="_blank" >10.1016/j.jde.2015.12.035</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Traveling waves in the nonlocal KPP-Fisher equation: Different roles of the right and the left interactions

Popis výsledku v původním jazyce

We consider the nonlocal KPP-Fisher equation ut(t, x)=uxx(t, x)+u(t, x)(1-(K*u)(t, x)) which describes the evolution of population density u(t, x) with respect to time t and location x. The non-locality is expressed in terms of the convolution of u(t,⋅) with kernel K(⋅)≥0, ∫RK(s)ds=1. The restrictions K(s), s≥0, and K(s), s≤0, are responsible for interactions of an individual with his left and right neighbors, respectively. We show that these two parts of K play quite different roles as for the existence and uniqueness of traveling fronts to the KPP-Fisher equation. In particular, if the left interaction is dominant, the uniqueness of fronts can be proved, while the dominance of the right interaction can induce the co-existence of monotone and oscillating fronts. We also present a short proof of the existence of traveling waves without assuming various technical restrictions usually imposed on K.

Název v anglickém jazyce

Traveling waves in the nonlocal KPP-Fisher equation: Different roles of the right and the left interactions

Popis výsledku anglicky

We consider the nonlocal KPP-Fisher equation ut(t, x)=uxx(t, x)+u(t, x)(1-(K*u)(t, x)) which describes the evolution of population density u(t, x) with respect to time t and location x. The non-locality is expressed in terms of the convolution of u(t,⋅) with kernel K(⋅)≥0, ∫RK(s)ds=1. The restrictions K(s), s≥0, and K(s), s≤0, are responsible for interactions of an individual with his left and right neighbors, respectively. We show that these two parts of K play quite different roles as for the existence and uniqueness of traveling fronts to the KPP-Fisher equation. In particular, if the left interaction is dominant, the uniqueness of fronts can be proved, while the dominance of the right interaction can induce the co-existence of monotone and oscillating fronts. We also present a short proof of the existence of traveling waves without assuming various technical restrictions usually imposed on K.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

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

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

260

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

6130-6175

Kód UT WoS článku

000374510900024

EID výsledku v databázi Scopus

2-s2.0-84958110692