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

Abstract

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 $L^{\infty }$. The article finally exhibits some time asymptotics properties of the solutions.

20 pages