Algal growth dynamics under light interaction: A nonlinear evolution problem

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