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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/8906

Title: Monotone traveling wavefronts of the KPP-Fisher delayed equation
Authors: Gomez, A.
Trofimchuk, S.
Keywords: KPP-Fisher delayed reaction-diffusion equation
Heteroclinic solutions
Monotone positive traveling wave
Existence
Uniqueness
Issue Date: Feb-2011
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: JOURNAL OF DIFFERENTIAL EQUATIONS Volume: 250 Issue: 4 Pages: 1767-1787 DOI: 10.1016/j.jde.2010.11.011
Abstract: In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation u(t)(t, x) = Delta u(t, x) + u (t, x)(1 - u(t - h, x)), u >= 0, x is an element of R(m). (*) Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in Eq. (*). We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach. (c) 2010 Elsevier Inc. All rights reserved.
Description: Trofimchuk, S (reprint author), Univ Talca, Inst Matemat & Fis, Casilla 747, Talca, Chile.
URI: http://dspace.utalca.cl/handle/1950/8906
ISSN: 0022-0396
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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