Invasion traveling wave solutions in temporally discrete random-diffusion systems with delays

Hui Xue; Jianhua Huang; Zhixian Yu

doi:10.3934/dcdss.2017060

Article Contents

2017, Volume 10, Issue 5: 1107-1131. Doi: 10.3934/dcdss.2017060

This issue Previous Article On concentration of semi-classical solitary waves for a generalized Kadomtsev-Petviashvili equation Next Article Lyapunov-type inequalities and solvability of second-order ODEs across multi-resonance

Invasion traveling wave solutions in temporally discrete random-diffusion systems with delays

1.
College of Science, National University of Defense Technology, Changsha 410073, China
2.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

^* Corresponding author: Jianhua Huang
^* Corresponding author: Jianhua Huang

Received: November 30, 2016

Revised: December 31, 2016

Published: October 2017

* The first two authors are supported by the NSF of China(No.11371367,11571126), and the third author is supported by Innovation Program of Shanghai Municipal Education Commission (No.14YZ096) and by the Hujiang Foundation of China (B14005)

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Abstract

This paper is devoted to the invasion traveling wave solutions for a temporally discrete delayed reaction-diffusion competitive system. The existence of invasion traveling wave solutions is established by using Schauder's fixed point Theorem. Ikeharaś theorem is applied to show the asymptotic behaviors. We further investigate the monotonicity and uniqueness invasion traveling waves with the help of sliding method and strong maximum principle.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35R10.

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