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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/10056

Title: Separation dichotomy and wavefronts for a nonlinear convolution equation
Authors: Gomez, C.
Prado, H.
Trofimchuk, S.
Keywords: Convolution
Monostable equation
Asymmetric non-local response
Stage structured population
Issue Date: 1-Dec-2014
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 420(1):1-19
Abstract: This paper is concerned with a scalar nonlinear convolution equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the convolution equation. Finally, we apply our theoretical results to several well-studied classes of evolution equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these equations can possess simultaneously stationary, expansion and extinction waves. (C) 2014 Elsevier Inc. All rights reserved.
Description: Trofimchuk, S (Trofimchuk, Sergei) Univ Talca, Inst Matemat & Fis,
URI: http://dspace.utalca.cl/handle/1950/10056
ISSN: 0022-247X
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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