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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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