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Wave propagation for a class of non-local dispersal non-cooperative systems

Part of: Linear integral equations Systems of linear integral equations Parabolic equations and systems Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  14 March 2019

Fei-Ying Yang ,
Wan-Tong Li  and
Jia-Bing Wang
Fei-Ying Yang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, China (wtli@lzu.edu.cn)
Wan-Tong Li
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, China (wtli@lzu.edu.cn)
Jia-Bing Wang
Affiliation:
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan430074, China
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Abstract

This paper is concerned with the travelling waves for a class of non-local dispersal non-cooperative system, which can model the prey-predator and disease-transmission mechanism. By the Schauder's fixed-point theorem, we first establish the existence of travelling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations, whose bounds are deduced from a precise analysis. Further, we characterize the minimal wave speed of travelling waves and obtain the non-existence of travelling waves with slow speed. Finally, we apply the general results to an epidemic model with bilinear incidence for its propagation dynamics.

Keywords

nonlocal dispersalprey-predator modelsminimal wave speedtraveling waves

MSC classification

Primary: 35K57: Reaction-diffusion equations 47G20: Integro-differential operators 92D25: Population dynamics (general)
Secondary: 45F05: Systems of nonsingular linear integral equations 45A05: Linear integral equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 4 , August 2020 , pp. 1965 - 1997
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Copyright
Copyright © Royal Society of Edinburgh 2019

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