Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity

Zhenguo Bai; Tingting Zhao

doi:10.3934/dcdsb.2018126

Article Contents

2018, Volume 23, Issue 10: 4063-4085. Doi: 10.3934/dcdsb.2018126

This issue Previous Article Next Article Time asymptotics of structured populations with diffusion and dynamic boundary conditions

Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity

Zhenguo Bai^1, and
Tingting Zhao^2,

1.
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710126, China
2.
School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China

Received: May 31, 2017

Revised: September 30, 2017

Early access: April 2018

Published: September 2018

The first author was supported by the NSF of China (11401453,11671315). The second author was supported by the NSF of China (11501446), Natural Science Research Fund of Northwest University (14NW17), and Scientific Research Plan Projects of Education Department of Shaanxi Provincial Government (15JK1765).

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Abstract

A non-local delayed reaction-diffusion model with a quiescent stage is investigated. It is shown that the spreading speed of this model without quasi-monotonicity is linearly determinate and coincides with the minimal wave speed of traveling waves.

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Mathematics Subject Classification: Primary: 35K57, 92D25; Secondary: 35R10.

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