Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations

Shi-Liang Wu; Tong-Chang Niu; Cheng-Hsiung Hsu

doi:10.3934/dcds.2017147

Article Contents

2017, Volume 37, Issue 6: 3467-3486. Doi: 10.3934/dcds.2017147

This issue Previous Article Asymptotic stability of stationary solutions for magnetohydrodynamic equations Next Article Global exponential κ-dissipative semigroups and exponential attraction

Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations

1.
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071, China
2.
Department of Mathematics, National Central University, Chungli 32001, Taiwan

Corresponding author
Corresponding author

Received: March 31, 2016

Revised: December 31, 2016

Published: May 2017

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Abstract

In this work we consider the global asymptotic stability of pushed traveling fronts for one-dimensional monostable reaction-diffusion equations with monotone delayed reactions. Pushed traveling front is a special type of critical wave front which converges to zero more rapidly than the near non-critical wave fronts. Recently, Trofimchuk et al. [16] proved the existence and uniqueness of pushed traveling fronts of the considered equation when the reaction term lost the sub-tangency condition. In this article, using the comparison method via a pair of super-and sub-solution and squeezing technique, we prove that the pushed traveling fronts are globally exponentially stable. This also gives an affirmative answer to an open problem presented by Solar and Trofimchuk [14].

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Mathematics Subject Classification: Primary: 35K57; Secondary: 92D25, 35B40.

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