Algae‐Light Interaction: Study Of An Approximated Model And Asymptotic Analysis

In this paper we study the approximation of a mathematical model for the interaction of algae with light consisting of two integro‐differential equations. In particular, we integrate the system in a suitable way and we get an autonomous system of ordinary differential equations. We discuss the equilibrium solutions and study their stability. We also make an asymptotic analysis by applying the modified Chapman‐Enskog procedure.

Keywords:

• Balance equations
• Equilibrium solutions
• Asymptotic analysis
• Chapman‐Enskog procedure

Acknowledgments

This work was partially supported by Par 2004 ‐ Research Project “Nuovi approcci matematici per lo studio di problemi in biologia, medicina, trasporto di fotoni e finanza” of the University of Siena funds as well as by MURST research funds. The authors would like to thank the unknown referees for the useful comments and suggestions, which helped to improve the exposition of the results. This paper is dedicated to Professor J. Mika for his 70th birthday.