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Transition waves for lattice Fisher-KPP equations with time and space dependence

Part of: Representations of solutions Infinite-dimensional dissipative dynamical systems Partial differential equations Functional-differential and differential-difference equations

Published online by Cambridge University Press:  28 April 2020

Ning Wang ,
Zhi-Cheng Wang  and
Xiongxiong Bao
Ning Wang
Affiliation:
School Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, People's Republic of China (nwang15@lzu.edu.cn; wangzhch@lzu.edu.cn)
Zhi-Cheng Wang
Affiliation:
School Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, People's Republic of China (nwang15@lzu.edu.cn; wangzhch@lzu.edu.cn)
Xiongxiong Bao
Affiliation:
School of Science, Chang'an University, Xi'an, Shaanxi710064, People's Republic of China (baoxx2016@chd.edu.cn)
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Abstract

This paper is concerned with the existence results for generalized transition waves of space periodic and time heterogeneous lattice Fisher-KPP equations. By constructing appropriate subsolutions and supersolutions, we show that there is a critical wave speed such that a transition wave solution exists as soon as the least mean of wave speed is above this critical speed. Moreover, the critical speed we construct is proved to be minimal in some particular cases, such as space-time periodic or space independent.

Keywords

Lattice differential equationsgeneralized transition wavesspace periodictime heterogeneous

MSC classification

Primary: 34K31: Lattice functional-differential equations
Secondary: 37L60: Lattice dynamics 35B51: Comparison principles 35C07: Traveling wave solutions 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 2 , April 2021 , pp. 573 - 600
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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