Traveling wave solutions in advection hyperbolic-parabolic system with nonlocal delay

Kun Li; Jianhua Huang; Xiong Li

doi:10.3934/dcdsb.2018227

Article Contents

2018, Volume 23, Issue 6: 2091-2119. Doi: 10.3934/dcdsb.2018227

This issue Previous Article Epidemic dynamics on complex networks with general infection rate and immune strategies Next Article Analysis of a Lévy-diffusion Leslie-Gower predator-prey model with nonmonotonic functional response

Traveling wave solutions in advection hyperbolic-parabolic system with nonlocal delay

1.
School of Mathematics and Computational Science, Hunan First Normal University, Changsha, 410205, China
2.
College of Science, National University of Defense Technology, Changsha, 410073, China
3.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

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

Received: June 2016

Revised: May 2018

Early access: July 2018

Published: June 2018

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Abstract

This paper is concerned with a class of advection hyperbolic-parabolic systems with nonlocal delay. We prove that the wave profile is described by a hybrid system that consists of an integral transformation and an ordinary differential equation. By considering the same problem for a properly parameterized system and the continuous dependence of the wave speed on the parameter involved, we obtain the existence and uniqueness of traveling wave solutions in advection hyperbolic-parabolic system with nonlocal delay under bistable assumption. The influence of advection on the propagation speed is also considered.

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Mathematics Subject Classification: Primary: 35R09, 35K46, 58D25.

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