Dataciencia

Colección SciELO Chile

WAVEFRONT'S STABILITY WITH ASYMPTOTIC PHASE IN THE DELAYED MONOSTABLE EQUATIONS

Indexado

WoS	WOS:000808167000001
Scopus	SCOPUS_ID:85137651752

DOI

10.1090/PROC/15988

Año

2022

Tipo

artículo de investigación

Citas Totales

Autores Afiliación Chile

Instituciones Chile

% Participación
Internacional

Autores
Afiliación Extranjera

Instituciones
Extranjeras

Abstract

We extend the class of initial conditions for scalar delayed reaction-diffusion equations ut(t, x) = uxx(t, x) + f(u(t, x), u(t − h, x)) which evolve in solutions converging to monostable traveling waves. Our approach allows to compute, in the moving reference frame, the phase distortion α of the limiting travelling wave with respect to the position of solution at the initial moment t = 0. In general, α ≠ 0 for the Mackey-Glass type diffusive equation. Nevertheless, α = 0 for the KPP-Fisher delayed equation: the related theorem also improves existing stability conditions for this model.

Revista

Revista	ISSN
Proceedings Of The American Mathematical Society	0002-9939

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Disciplinas de Investigación

WOS
Mathematics
Mathematics, Applied

Scopus
Sin Disciplinas

SciELO
Sin Disciplinas

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Publicaciones WoS (Ediciones: ISSHP, ISTP, AHCI, SSCI, SCI), Scopus, SciELO Chile.

Colaboración Institucional

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Autores - Afiliación

Ord.	Autor	Género	Institución - País
1	Solar, Abraham	Hombre	Universidad Católica de la Santísima Concepción - Chile
2	Trofimchuk, S.	Hombre	Universidad de Talca - Chile

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Financiamiento

Fuente
Fondo Nacional de Desarrollo Científico y Tecnológico
FONDECYT (Chile)

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Agradecimientos

Agradecimiento
Received by the editors July 25, 2021, and, in revised form, December 23, 2021. 2020 Mathematics Subject Classification. Primary 35C07, 35R10; Secondary 35K57. Key words and phrases. Monostable equation, delay, traveling front, non-monotone response. This work was supported by FONDECYT (Chile), projects 11190350 (A.S.), 1190712 (S.T.). The authors express their gratitude to the anonymous referee, whose valuable comments helped to improve the original version of this paper. The second author is the corresponding author. 1Bydefinition,theprofileφshouldsatisfyφ(−∞)=0,liminft→+∞φ(t)>0,supt∈Rφ(t)<∞. 2We assume everywhere that (i) u0(s, x) is bounded, globally Lipschitz continuous in x (uniformly in s) and (ii) the solution u(t, x) exists globally and is bounded on the strips [0,n]×R,n ∈ N. Note that (ii) is satisfied automatically for both models (KPP-Fisher and Nicholson’s) of the paper.
This work was supported by FONDECYT (Chile), projects 11190350 (A.S.), 1190712 (S.T.).

Agradecimiento

Received by the editors July 25, 2021, and, in revised form, December 23, 2021. 2020 Mathematics Subject Classification. Primary 35C07, 35R10; Secondary 35K57. Key words and phrases. Monostable equation, delay, traveling front, non-monotone response. This work was supported by FONDECYT (Chile), projects 11190350 (A.S.), 1190712 (S.T.). The authors express their gratitude to the anonymous referee, whose valuable comments helped to improve the original version of this paper. The second author is the corresponding author. 1Bydefinition,theprofileφshouldsatisfyφ(−∞)=0,liminft→+∞φ(t)>0,supt∈Rφ(t)<∞. 2We assume everywhere that (i) u0(s, x) is bounded, globally Lipschitz continuous in x (uniformly in s) and (ii) the solution u(t, x) exists globally and is bounded on the strips [0,n]×R,n ∈ N. Note that (ii) is satisfied automatically for both models (KPP-Fisher and Nicholson’s) of the paper.

This work was supported by FONDECYT (Chile), projects 11190350 (A.S.), 1190712 (S.T.).