Existence, uniqueness of solutions to a coupled ODE-PDE model of invasive tree species, and stability of steady state solutions

Efendiev M., Ôtani M., Sivaloganathan S.

Journal of Mathematical Analysis and Applications, vol.559, no.1, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 559 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1016/j.jmaa.2026.130418
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Coupled ODE-PDE system, Existence-uniqueness, L∞-energy method, Stability of solutions
  • Marmara University Affiliated: No

Abstract

In a recent paper, E. Hughes et al. introduced a coupled ODE-PDE model to study the propagation of invasive tree species. These species, often originating from the Pinacea family, have had a demonstrably negative impact on grassland ecosystems worldwide (particularly in regions such as New Zealand, South Africa, and Chile). In this paper, we apply the classical subdifferential operator theory due to H. Brézis [1] to establish existence and uniqueness of solutions to the coupled ODE-PDE model for studying the propagation of invasive tree species in grassland ecosystems. Ensuring precise prediction of invasive tree population behaviour in grasslands is critical for effective invasive species management. To this purpose, we further prove the existence of a unique stationary state and discuss its stability. In this process, L∞-energy method plays a crucial role. A subsequent study will delve into the long-term dynamics of the model, investigating the existence of travelling wave solutions in unbounded domains.