%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Perasso, A.
%A Richard, Quentin
%A Azzali, I.
%A Venturino, E.
%T Well-posedness, positivity, and time asymptotics properties for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity
%D 2021
%L fdi:010079856
%G ENG
%J Studies in Applied Mathematics
%@ 0022-2526
%K plankton modeling ; positivity ; predator-prey models ; reaction-diffusion models ; well-posedness
%M ISI:000579426700001
%N 1
%P 211-232
%R 10.1111/sapm.12345
%U https://www.documentation.ird.fr/hor/fdi:010079856
%> https://www.documentation.ird.fr/intranet/publi/2020/11/010079856.pdf
%V 146
%W Horizon (IRD)
%X 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.
%$ 034 ; 020