Spatial propagation in nonlocal dispersal Fisher-KPP equations
Xu, Wen-Bing1,2; Li, Wan-Tong1; Ruan, Shigui3
AbstractIn this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and f'(0), where f is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new "forward-backward spreading" method. Third, we investigate the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponential decay rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details on the influence of asymmetric dispersal. (C) 2021 Elsevier Inc. All rights reserved.
KeywordNonlocal dispersal Fisher-KPP equation Spatial propagation Spreading speed Asymmetric kernel
Indexed BySCI
Funding ProjectChina Postdoctoral Science Foundation[2019M660047] ; NSF of China[11731005] ; National Science Foundation[DMS-1853622]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000629298100001
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Document Type期刊论文
Corresponding AuthorLi, Wan-Tong
Affiliation1.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Miami, Dept Math, Coral Gables, FL 33146 USA
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GB/T 7714
Xu, Wen-Bing,Li, Wan-Tong,Ruan, Shigui. Spatial propagation in nonlocal dispersal Fisher-KPP equations[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2021,280(10):35.
APA Xu, Wen-Bing,Li, Wan-Tong,&Ruan, Shigui.(2021).Spatial propagation in nonlocal dispersal Fisher-KPP equations.JOURNAL OF FUNCTIONAL ANALYSIS,280(10),35.
MLA Xu, Wen-Bing,et al."Spatial propagation in nonlocal dispersal Fisher-KPP equations".JOURNAL OF FUNCTIONAL ANALYSIS 280.10(2021):35.
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