Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach

Qian Liu, Shuang Liu, King Yeung Lam*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we derive the exact spreading speeds and prove the convergence to homogeneous equilibrium states between successive invasion fronts. Our method is inspired by the geometric optics approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. Our main result settles an open question raised by Shigesada et al. in 1997, and shows that one of the species spreads to the right with a nonlocally pulled front.

Original languageEnglish
Pages (from-to)3683-3714
Number of pages32
JournalDiscrete and Continuous Dynamical Systems
Volume40
Issue number6
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Compacted support
  • Competition
  • Geometric optics
  • Hamilton-Jacobi equation
  • Spreading

Fingerprint

Dive into the research topics of 'Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach'. Together they form a unique fingerprint.

Cite this