Uniqueness and stability of time-periodic pyramidal fronts for a periodic competition-diffusion system

Xiongxiong Bao; Wan-Tong Li; Zhi-Cheng Wang

doi:10.3934/cpaa.2020014

Article Contents

2020, Volume 19, Issue 1: 253-277. Doi: 10.3934/cpaa.2020014

This issue Previous Article Positive solutions for the one-dimensional singular superlinear

$ p $

-Laplacian problem Next Article Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian

Uniqueness and stability of time-periodic pyramidal fronts for a periodic competition-diffusion system

1.
School of Science, Chang'an University, Xi'an, Shaanxi 710064, China
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China

^* Corresponding author
^* Corresponding author

Received: November 2018

Revised: April 2019

Published: July 2019

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Abstract

The existence, non-existence and qualitative properties of time periodic pyramidal traveling front solutions for the time periodic Lotka-Volterra competition-diffusion system have already been studied in $ \Bbb{R}^{N} $ with $ N\geq 3 $. In this paper, we continue to study the uniqueness and asymptotic stability of such time-periodic pyramidal traveling front in the three-dimensional whole space. For any given admissible pyramid, we show that the time periodic pyramidal traveling front is uniquely determined and it is asymptotically stable under the condition that given perturbations decay at infinity. Moreover, the time periodic pyramidal traveling front is uniquely determined as a combination of two-dimensional periodic V-form waves on the edges of the pyramid.

Keywords:

Lotka-Volterra competition-diffusion system,
time-periodic,
pyramidal traveling fronts,
uniqueness,
stability.

Mathematics Subject Classification: 35K40, 35C07, 35B10, 35B35, 35B40.

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