Spreading speeds and monostable waves in a reaction-diffusion model with nonlinear competition

Qiming Zhang, Yazhou Han, Wim T. van Horssen, Manjun Ma*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper the wave propagation dynamics of a Lotka-Volterra type of model with cubic competition is studied. The existence of traveling waves and the uniqueness of spreading speeds are established. It is also shown that the spreading speed is equal to the minimal speed for traveling waves. Furthermore, general conditions for the linear or nonlinear selection of the spreading speed are obtained by using the comparison principle and the decay characteristics for traveling waves. By constructing upper solutions, explicit conditions to determine the linear selection of the spreading speed are derived.

Original languageEnglish
Article number126077
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume511
Issue number2
DOIs
Publication statusPublished - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Cubic competition
  • Linear selection
  • Lotka-Volterra model
  • Minimal wave speed
  • Spreading speed

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