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January 2016, 15(1): 139-160. doi: 10.3934/cpaa.2016.15.139
Curved fronts of monostable reaction-advection-diffusion equations in space-time periodic media
Zhen-Hui Bu 1, and Zhi-Cheng Wang 2,
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000
Received July 2015 Revised September 2015 Published December 2015
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 $N\geq4$.
Keywords: reaction-advection-diffusion equations, Curved fronts, space-time periodic., minimal speed.
Mathematics Subject Classification: 35K57, 35C07, 35B35, 35B4.
Citation: Zhen-Hui Bu, Zhi-Cheng Wang. Curved fronts of monostable reaction-advection-diffusion equations in space-time periodic media. Communications on Pure & Applied Analysis, 2016, 15 (1) : 139-160. doi: 10.3934/cpaa.2016.15.139
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Zhen-Hui Bu Zhi-Cheng Wang