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Stability analysis of the phytoplankton vertical steady states in a laboratory test tube
Author(s) -
Beretta Edoardo,
Fasano Antonio,
Hosono Yuzo,
Kolmanovskii V. B.
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170705
Subject(s) - mathematics , corollary , stability (learning theory) , sobolev space , norm (philosophy) , population , mathematical analysis , pure mathematics , demography , machine learning , sociology , computer science , political science , law
The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H 2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro‐differential equations.