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August, 2020 Global Stability of Non-monotone Noncritical Traveling Waves for a Discrete Diffusion Equation with a Convolution Type Nonlinearity
Tao Su, Guo-Bao Zhang
Taiwanese J. Math. 24(4): 937-957 (August, 2020). DOI: 10.11650/tjm/190901

Abstract

This paper is concerned with the global stability of non-monotone traveling waves for a discrete diffusion equation with a monostable convolution type nonlinearity. It has been proved by Yang and Zhang (Sci. China Math. 61 (2018), 1789--1806) that all noncritical traveling waves (waves with speeds $c \gt c_*$, $c_*$ is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. In this paper, we further prove that all traveling waves with large speed are globally stable, when the initial perturbations around the waves in a weighted Sobolev space can be arbitrarily large. The approaches adopted are the nonlinear Halanay's inequality, the technical weighted energy method and Fourier's transform.

Citation

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Tao Su. Guo-Bao Zhang. "Global Stability of Non-monotone Noncritical Traveling Waves for a Discrete Diffusion Equation with a Convolution Type Nonlinearity." Taiwanese J. Math. 24 (4) 937 - 957, August, 2020. https://doi.org/10.11650/tjm/190901

Information

Received: 18 January 2019; Revised: 20 June 2019; Accepted: 1 September 2019; Published: August, 2020
First available in Project Euclid: 9 September 2019

MathSciNet: MR4124552
Digital Object Identifier: 10.11650/tjm/190901

Subjects:
Primary: 35C07, 35K57, 92D25

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 4 • August, 2020
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