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Efendiyev, M.A. ; M. Ôtani,* ; Sivaloganathan, S.*

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

J. Math. Anal. Appl. 559, 130418 - 130418 (2026)
DOI
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.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Coupled Ode-pde System ; Existence-uniqueness ; L∞-energy Method ; Stability Of Solutions; Demography
ISSN (print) / ISBN 0022-247X
e-ISSN 1096-0813
Zeitschrift Journal of Mathematical Analysis and Applications
Quellenangaben Band: 559, Heft: 1, Seiten: 130418 - 130418 Artikelnummer: , Supplement: ,
Verlag Elsevier
Verlagsort 525 B St, Ste 1900, San Diego, Ca 92101-4495 Usa
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen Ministry of Education, Culture, Sports, Science and Technology, Japan
National Science and Engineering Research Council (NSERC)
University of Canterbury for an Erskine Fellowship