Exponential stability of traveling wavefronts for a system modeling the geographic spread of black-legged tick Ixodes scapularis

This paper is concerned with the exponential stability of traveling wavefronts for a system modeling the geographic spread of black-legged tick Ixodes scapularis . It is shown in a recent work (Lai and Zou in J Differ Equ 269: 6400-6421, 2020) that this system admits traveling wavefronts when the ba...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-06, Vol.74 (3), Article 116
Main Authors: Hao, Yu-Cai, Zhang, Guo-Bao, He, Juan
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Energy methods
Engineering
Mathematical Methods in Physics
Modelling
Perturbation
Stability
Theoretical and Applied Mechanics
Wave fronts
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Summary:This paper is concerned with the exponential stability of traveling wavefronts for a system modeling the geographic spread of black-legged tick Ixodes scapularis . It is shown in a recent work (Lai and Zou in J Differ Equ 269: 6400-6421, 2020) that this system admits traveling wavefronts when the basic reproduction number is greater than one and the wave speeds are larger than or equal to the asymptotic speed of spread. In this paper, we further study the asymptotic stability of traveling wavefronts. Applying the techniques of weighted energy method and the comparison principle, we prove that the traveling wavefronts with relatively large speed are exponentially stable, when the initial perturbation around the traveling wavefronts decays exponentially as x → - ∞ , but can be arbitrarily large in other locations.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-023-02014-9