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

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.