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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 2395 - 2430, Volume 37, Issue 5, May 2017      doi:10.3934/dcds.2017104

 
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Zhen-Hui Bu - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)
Zhi-Cheng Wang - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)

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.

Keywords:  Pyramidal traveling front, reaction diffusion equation, degenerate monostable nonlinearity, combustion nonlinearity, stability.
Mathematics Subject Classification:  Primary: 35B35, 35K57; Secondary: 35K55.

Received: July 2016;      Revised: December 2016;      Available Online: February 2017.

 References