Taiwanese Journal of Mathematics

Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay

Xin Wu, Zhaohai Ma, and Rong Yuan

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 21, Number 6 (2017), 1381-1411.

Dates
Received: 13 October 2016
Revised: 19 March 2017
Accepted: 27 March 2017
First available in Project Euclid: 17 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1502935243

Digital Object Identifier
doi:10.11650/tjm/8048

Mathematical Reviews number (MathSciNet)
MR3732911

Zentralblatt MATH identifier
06871374

Subjects
Primary: 35R10: Partial functional-differential equations 35B40: Asymptotic behavior of solutions 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 58D25: Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]

Keywords
stability delayed reaction diffusion system traveling waves weighted energy method

Citation

Wu, Xin; Ma, Zhaohai; Yuan, Rong. Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay. Taiwanese J. Math. 21 (2017), no. 6, 1381--1411. doi:10.11650/tjm/8048. https://projecteuclid.org/euclid.twjm/1502935243


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