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

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 exi...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 151; no. 2; pp. 573 - 600
Main Authors Wang, Ning, Wang, Zhi-Cheng, Bao, Xiongxiong
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.04.2021
Cambridge University Press
Subjects
Mathematical analysis
generalized transition waves
Lattice differential equations
time heterogeneous
37L60
35B51
35B40
space periodic
34K31
35C07
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2020.31