Spreading speeds for a class of non-local convolution differential equation

Zhaoquan Xu; Chufen Wu

doi:10.3934/dcdsb.2020108

Article Contents

2020, Volume 25, Issue 11: 4479-4492. Doi: 10.3934/dcdsb.2020108

This issue Previous Article Mathematical analysis of an age structured heroin-cocaine epidemic model Next Article Almost sure exponential stabilization and suppression by periodically intermittent stochastic perturbation with jumps

Spreading speeds for a class of non-local convolution differential equation

Zhaoquan Xu^1, and
Chufen Wu^2, ,

1.
Department of Mathematics, Jinan University, Guangzhou 510632, China
2.
School of Mathematics and Big Data, Foshan University, Foshan 528000, China

^* Corresponding author: chufenwu@126.com
^* Corresponding author: chufenwu@126.com

Received: December 31, 2018

Revised: October 31, 2019

Early access: March 2020

Published: November 2020

The first author is supported by NSF of China grant No. 11701216, NSF of Guangdong Province grant No. 2017A030313015 and the Fundamental Research Funds for the Central Universities. The second author is supported by NSF of Guangdong Province grant No. 2019A1515011648 and NSF of China grant No. 11401096

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Abstract

The spatial spreading dynamics is considered for a class of convolution differential equation resulting from physical and biological problems. It is shown that this kind of equation with monostable structure admits a spreading speed, even when the nonlinear reaction terms without monotonicity. The upward convergence of spreading speed is also established under appropriate conditions.

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Mathematics Subject Classification: Primary: 45J05, 35R10; Secondary: 92A05.

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