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Algal growth dynamics under light interaction: A nonlinear evolution problem

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Abstract

A mathematical model for interaction of algae with light is presented. This model consists of a couple of nonlinear integro-differential equations dealing with the evolution of algae concentration due to absorption of light and the evolution of light intensity due to absorption and scattering by algae and water. The model is formulated as a nonlinear abstract Cauchy problem in a Banach space suited to describe the physical features of the problem. By using techniques and results of semigroups theory, it is proved that the system has a unique global strict solution.

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References

  1. Atti, del Convegno su: Prospettive della Coltura della Spirulina in Italia, Firenze, 20–21 Nov. 1980

  2. Belleni Morante, A.: Applied semigroups and evolution equations. Oxford: Clarendon Press, 1979

    Google Scholar 

  3. Kato, T.: Perturbation theory for linear operators. New York: Springer, 1966

    Google Scholar 

  4. Martin, R. H., Jr.: Nonlinear operators and differential equations in Banach spaces. New York: J. Wiley, 1976

    Google Scholar 

  5. Morton, R.: A model for light-scattering by algae in water. Math. Biosci. 40, 195–204 (1978)

    Google Scholar 

  6. Okubo, A.: Private Communication

  7. Pomraning, G. C.: The equation of radiation hydrodynamics. Oxford: Pergamon Press, 1973

    Google Scholar 

  8. Shigesada, N., Okubo, A.: Analysis of the self-shading effect on algal vertical distribution in natural waters. J. Math. Biol. 12, 311–326 (1981)

    Google Scholar 

  9. Totaro, S.; On a nonlinear problem arising from interaction of algae with light. In: Proceedings of the Conference Mathematics in Biology and Medicine. Bari, July 1983 (to appear)

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Authors and Affiliations

  1. “Giovanni Sansone”, Istituto di Matematica Applicata, Via S. Marta, 3, 3-50139, Firenze, Italy

    Silvia Totaro

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  1. Silvia Totaro
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Work performed under the auspices of G.N.F.M. (Gruppo Nazionale per la Fisica Matematica)

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Totaro, S. Algal growth dynamics under light interaction: A nonlinear evolution problem. J. Math. Biology 20, 185–201 (1984). https://doi.org/10.1007/BF00285346

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  • DOI: https://doi.org/10.1007/BF00285346

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