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A scaled nonlinear mathematical model for interaction of algae with light: Existence and uniqueness results. (English) Zbl 0923.92026
Summary: We study the mathematical properties of a scaled nonlinear model for interaction of algae with light. The growth dynamics is modeled by a couple of nonlinear equations for the evolution of the concentration of algae and the light intensity, in a column of water. A diffusion model is derived applying formally the modified Chapman-Enskog expansion to the Boltzmann-like evolution system for a small parameter \(\varepsilon\), proportional to the average time between successive photon-water collisions. Existence and uniqueness of a positive solution are proved, using semigroup perturbation theory.

92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
82C70 Transport processes in time-dependent statistical mechanics
46N60 Applications of functional analysis in biology and other sciences
35B20 Perturbations in context of PDEs
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