@article{d2273bfb1a99422bbce736fa0d804675,
title = "Spatial propagation in nonlocal dispersal Fisher-KPP equations",
abstract = "In 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.",
keywords = "Asymmetric kernel, Nonlocal dispersal Fisher-KPP equation, Spatial propagation, Spreading speed",
author = "Xu, {Wen Bing} and Li, {Wan Tong} and Shigui Ruan",
note = "Funding Information: The authors would like to thank Prof. Chris Cosner (University of Miami), Prof. Jian-Wen Sun (Lanzhou University), Dr. Ru Hou (Peking University) and Dr. Teng-Long Cui (Lanzhou University) for their helpful comments. The authors are also grateful to the anonymous reviewer for his/her constructive comments and helpful suggestions. Research of W.-B. Xu was partially supported by China Postdoctoral Science Foundation ( 2019M660047 ); research of W.-T. Li was partially supported by NSF of China ( 11731005 ); and research of S. Ruan was partially supported by National Science Foundation ( DMS-1853622 ). Funding Information: The authors would like to thank Prof. Chris Cosner (University of Miami), Prof. Jian-Wen Sun (Lanzhou University), Dr. Ru Hou (Peking University) and Dr. Teng-Long Cui (Lanzhou University) for their helpful comments. The authors are also grateful to the anonymous reviewer for his/her constructive comments and helpful suggestions. Research of W.-B. Xu was partially supported by China Postdoctoral Science Foundation (2019M660047); research of W.-T. Li was partially supported by NSF of China (11731005); and research of S. Ruan was partially supported by National Science Foundation (DMS-1853622). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = may,
day = "15",
doi = "10.1016/j.jfa.2021.108957",
language = "English (US)",
volume = "280",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "10",
}