Well‐posedness, positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities, involving a rational nonlinearity with singularity

Antoine Perasso (1) , Quentin Richard (2) , Irene Azzali (3) , Ezio Venturino (4)

1 LCE - Laboratoire Chrono-environnement (UMR 6249)
2 MIVEGEC - Maladies infectieuses et vecteurs : écologie, génétique, évolution et contrôle
3 UNITO - Università degli studi di Torino = University of Turin
4 Dipartimento di Matematica "Giuseppe Peano" [Torino]

In this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplanktons and zooplanktons. Using a semigroup approach in L 2 , we prove global existence, uniqueness and positivity of the solutions. The Holling type 2 nonlinearities, i.e of rational type with singularity, are handled by providing estimates in L ∞. The article finally exhibits some time asymptotics properties of the solutions.

Mots clés: Reaction-diffusion models; positivity; well-posedness; plankton modeling; predator-prey models

Domaines: Interactions entre organismes; Equations aux dérivées partielles [math.AP]

Antoine Perasso, Quentin Richard, Irene Azzali, Ezio Venturino. Well‐posedness, positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities, involving a rational nonlinearity with singularity. Studies in Applied Mathematics, 2021, 146 (1), pp.211-232. ⟨10.1111/sapm.12345⟩. ⟨hal-03881336v2⟩