Curved fronts of monostable reaction-advection-diffusion equations inspace-time periodic media

Zhen-Hui  Bu; Zhi-Cheng Wang

doi:10.3934/cpaa.2016.15.139

Article Contents

2016, Volume 15, Issue 1: 139-160. Doi: 10.3934/cpaa.2016.15.139

This issue Previous Article Riemann problem for the relativistic generalized Chaplygin Euler equations Next Article Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum

Curved fronts of monostable reaction-advection-diffusion equations in space-time periodic media

Zhen-Hui Bu^1, and
Zhi-Cheng Wang^2,

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000

Received: June 30, 2015

Revised: August 31, 2015

Published: December 2015

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Abstract

This paper is to study traveling fronts of reaction-diffusion equations with space-time periodic advection and nonlinearity in $\mathbb{R}^N$ with $N\geq3$. We are interested in curved fronts satisfying some ``pyramidal" conditions at infinity. In $\Bbb{R}^3$, we first show that there is a minimal speed $c^{*}$ such that curved fronts with speed $c$ exist if and only if $c\geq c^{*}$, and then we prove that such curved fronts are decreasing in the direction of propagation. Furthermore, we give a generalization of our results in $\mathbb{R}^N$ with $N\geq4$.

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Mathematics Subject Classification: 35K57, 35C07, 35B35, 35B40.

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