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2013 EXISTENCE, ASYMPTOTICS AND UNIQUENESS OF TRAVELING WAVES FOR NONLOCAL DIFFUSION SYSTEMS WITH DELAYED NONLOCAL RESPONSE
Zhixian Yu, Rong Yuan
Taiwanese J. Math. 17(6): 2163-2190 (2013). DOI: 10.11650/tjm.17.2013.3794

Abstract

In this paper, we deal with the existence, asymptotic behavior and uniqueness of traveling waves for nonlocal diffusion systems with delay and global response. We first obtain the existence of traveling wave front by using upper-lower solutions method and Schauder's fixed point theorem for $c\gt c_*$ and using a limiting argument for $c=c_*$. Secondly, we find a priori asymptotic behavior of (monotone or non-monotone) traveling waves with the help of Ikehara's Theorem by constructing a Laplace transform representation of a solution. Thirdly, we show that the traveling wave front for each given wave speed is unique up to a translation. Last, we apply our results to two models with delayed nonlocal response.

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Zhixian Yu. Rong Yuan. "EXISTENCE, ASYMPTOTICS AND UNIQUENESS OF TRAVELING WAVES FOR NONLOCAL DIFFUSION SYSTEMS WITH DELAYED NONLOCAL RESPONSE." Taiwanese J. Math. 17 (6) 2163 - 2190, 2013. https://doi.org/10.11650/tjm.17.2013.3794

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1311.35053
MathSciNet: MR3141880
Digital Object Identifier: 10.11650/tjm.17.2013.3794

Subjects:
Primary: 35C07 , 35R10

Keywords: asymptotics , Delay , nonlocal diffusion , Traveling wave fronts

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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