Well‐posedness, positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities, involving a rational nonlinearity with singularity - Archive ouverte HAL Access content directly
Journal Articles Studies in Applied Mathematics Year : 2021

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

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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 ∞. The article finally exhibits some time asymptotics properties of the solutions.
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Dates and versions

hal-03881336 , version 1 (01-12-2022)
hal-03881336 , version 2 (08-12-2022)

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Antoine Perasso, Quentin Richard, Irene Azzali, Ezio Venturino. Well‐posedness, positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities, involving a rational nonlinearity with singularity. Studies in Applied Mathematics, 2021, 146 (1), pp.211-232. ⟨10.1111/sapm.12345⟩. ⟨hal-03881336v1⟩
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