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arXiv · 1902.00752

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

Antoine Perasso·Quentin Richard·Irene Azzali·Ezio Venturino
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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.

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Antoine Perasso, Quentin Richard, Irene Azzali, Ezio Venturino. 2019-02-02. Well-posedness and positivity property for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity. https://arxiv.org/abs/1902.00752

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