# American Institute of Mathematical Sciences

November  2020, 25(11): 4479-4492. doi: 10.3934/dcdsb.2020108

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

 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

Received  January 2019 Revised  November 2019 Published  November 2020 Early access  March 2020

Fund Project: 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

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.

Citation: Zhaoquan Xu, Chufen Wu. Spreading speeds for a class of non-local convolution differential equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4479-4492. doi: 10.3934/dcdsb.2020108
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