Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media

Jianping Gao; Shangjiang Guo; Wenxian Shen

doi:10.3934/dcdsb.2020199

Article Contents

2021, Volume 26, Issue 5: 2645-2676. Doi: 10.3934/dcdsb.2020199

This issue Previous Article Global classical solutions to two-dimensional chemotaxis-shallow water system Next Article Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks

Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media

1.
School of Mathematics, Hunan University, Changsha, Hunan 410082, China
2.
Department of Mathematics and Statistics, Auburn University, AL 36849, USA
3.
School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China

^* Corresponding author: Jianping Gao
^* Corresponding author: Jianping Gao

Received: November 30, 2019

Revised: March 31, 2020

Early access: June 2020

Published: May 2021

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Abstract

In this paper, we investigate the asymptotic dynamics of Fisher-KPP equations with nonlocal dispersal operator and nonlocal reaction term in time periodic and space heterogeneous media. We first show the global existence and boundedness of nonnegative solutions. Next, we obtain some sufficient conditions ensuring the uniform persistence. Finally, we study the existence, uniqueness and global stability of positive time periodic solutions under several different conditions.

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Mathematics Subject Classification: Primary: 47G20, 47J35, 92D25; Secondary: 35K57, 58D25.

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