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

Shi Liang Wu, Tong Chang Niu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 re-action 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].

Original languageEnglish
Pages (from-to)3467-3486
Number of pages20
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number6
DOIs
StatePublished - 2017

Keywords

  • Global asymptotic stability
  • Pushed traveling front
  • Squeezing technique
  • Sub- and super-solution method

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