Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations Ⅰ

Zhen-Hui Bu; Zhi-Cheng Wang

doi:10.3934/dcds.2017104

Article Contents

2017, Volume 37, Issue 5: 2395-2430. Doi: 10.3934/dcds.2017104

This issue Previous Article Homogenization of trajectory attractors of 3D Navier-Stokes system with randomly oscillating force Next Article Parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms

Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations Ⅰ

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: June 30, 2016

Revised: November 30, 2016

Published: May 2017

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Abstract

This paper is concerned with traveling curved fronts in reaction diffusion equations with degenerate monostable and combustion nonlinearities. For a given admissible pyramidal in three-dimensional spaces, the existence of a pyramidal traveling front has been proved by Wang and Bu [30] recently. By constructing new supersolutions and developing the arguments of Taniguchi [25] for the Allen-Cahn equation, in this paper we first characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces, and then establish the uniqueness and asymptotic stability of such three-dimensional pyramidal traveling fronts under the condition that given perturbations decay at infinity.

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

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