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December, 2017 Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay
Xin Wu, Zhaohai Ma, Rong Yuan
Taiwanese J. Math. 21(6): 1381-1411 (December, 2017). DOI: 10.11650/tjm/8048

Abstract

This paper is concerned with the nonlinear stability of traveling waves of a delayed monostable epidemic model with quasi-monotone condition. We prove that the traveling wave front is exponentially stable by means of the weighted-energy method and the comparison principle to perturbation in some exponentially weighted $L^{\infty}$ spaces, when the difference between initial data and traveling wave front decays exponentially as $x \to -\infty$, but the initial data can be suitable large in other locations. Finally, we present two examples to support our theoretical results.

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Xin Wu. Zhaohai Ma. Rong Yuan. "Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay." Taiwanese J. Math. 21 (6) 1381 - 1411, December, 2017. https://doi.org/10.11650/tjm/8048

Information

Received: 13 October 2016; Revised: 19 March 2017; Accepted: 27 March 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871374
MathSciNet: MR3732911
Digital Object Identifier: 10.11650/tjm/8048

Subjects:
Primary: 34K30 , 35B40 , 35R10 , 58D25

Keywords: delayed reaction diffusion system , stability , Traveling waves , weighted energy method

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 6 • December, 2017
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