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Well‐posedness, positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities, involving a rational nonlinearity with singularity
Author(s) -
Perasso Antoine,
Richard Quentin,
Azzali Irene,
Venturino Ezio
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12345
Subject(s) - uniqueness , semigroup , nonlinear system , mathematics , diffusion , work (physics) , singularity , reaction–diffusion system , zooplankton , plankton , statistical physics , mathematical analysis , ecology , physics , thermodynamics , biology , quantum mechanics
In this work, we consider a reaction–diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. Using a semigroup approach in L 2 , we prove global existence, uniqueness, and positivity of the solutions. The nonlinearity is handled by providing estimates in L ∞ , 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.