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