Global stability of V-shaped traveling fronts in combustion and degenerate monostable equations

Zhen-Hui Bu; Zhi-Cheng Wang

doi:10.3934/dcds.2018093

Article Contents

2018, Volume 38, Issue 5: 2251-2286. Doi: 10.3934/dcds.2018093

This issue Previous Article Decaying turbulence for the fractional subcritical Burgers equation Next Article Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems

Global stability of V-shaped traveling fronts in combustion and degenerate monostable equations

Zhen-Hui Bu and
Zhi-Cheng Wang^,

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

* Corresponding author: Z.-C. Wang
* Corresponding author: Z.-C. Wang

Received: March 31, 2017

Revised: November 30, 2017

Published: June 2018

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Abstract

This paper is concerned with the global stability of V-shaped traveling fronts in reaction-diffusion equations with combustion and degenerate monostable nonlinearity. The existence of such curved fronts has been recently proved by [39]. In this paper, by constructing new subsolutions, we show the asymptotic stability of V-shaped traveling fronts.

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Mathematics Subject Classification: Primary: 35B35, 35K57; Secondary: 35K55.

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Figure 1. The profiles of the traveling curved front $V$ and the thick solid curve shows the level line $V = 0.5$.

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Figure 2. The level sets of the traveling curved front $V$.

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