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Global dynamics and spreading speeds for a partially degenerate system with non-local dispersal in periodic habitats

Part of: Miscellaneous topics - Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  22 June 2018

Jia-Bing Wang ,
Wan-Tong Li  and
Jian-Wen Sun
Jia-Bing Wang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China (wtli@lzu.edu.cn)
Wan-Tong Li
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China (wtli@lzu.edu.cn)
Jian-Wen Sun
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China (wtli@lzu.edu.cn)
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Abstract

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This paper is concerned with the global dynamics and spreading speeds of a partially degenerate non-local dispersal system with monostable nonlinearity in periodic habitats. We first obtain the existence of the principal eigenvalue for a periodic eigenvalue problem with partially degenerate non-local dispersal. Then we study the coexistence and extinction dynamics. Finally, the existence and characterization of spreading speeds are considered. In particular, we show that the spreading speed is linearly determinate. Overall, we extend the existing results on global dynamics and spreading speeds for the degenerate reaction–diffusion system to the degenerate non-local dispersal case. The extension is non-trivial and meaningful.

Keywords

partially degenerate systemperiodic habitatnon-local dispersalglobal dynamicsspreading speeds

MSC classification

Secondary: 35K57: Reaction-diffusion equations 35R20: Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions) 92D25: Population dynamics (general)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 849 - 880
Copyright
Copyright © Royal Society of Edinburgh 2018