Perasso A., Richard Quentin, Azzali I., Venturino E. (2021). 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, 146 (1), 211-232. ISSN 0022-2526.
Titre du document
Well-posedness, positivity, and time asymptotics properties for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity
Perasso A., Richard Quentin, Azzali I., Venturino E.
Source
Studies in Applied Mathematics, 2021,
146 (1), 211-232 ISSN 0022-2526
In this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. Using a semigroup approach inL2, we prove global existence, uniqueness, and positivity of the solutions. The nonlinearity is handled by providing estimates inL infinity, allowing to deal with most of the functional responses that describe predator/prey interactions (Holling I, II, III, Ivlev) in ecology. The paper finally exhibits some time asymptotic properties of the solutions.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
;
Limnologie biologique / Océanographie biologique [034]
