Summary
A system of parabolic and ordinary differential equations u t = a 2 u xx + F(u, v, w), v t = a 2 v xx + G(u, v, w),w x = − k(u)w is studied which has been proposed by Radach and Maier-Reimer for the dynamics of phytoplankton and nutrient in dependence of light intensity. It is shown that there is a unique solution to this system satisfying given initial and boundary conditions. The solution depends continuously on the data. For specific nonlinearities F, G, and k bounds for the solutions are given.
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Wörz-Busekros, A. Solutions to a degenerate system of parabolic equations from marine biology. J. Math. Biol. 3, 393–406 (1976). https://doi.org/10.1007/BF00275068
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DOI: https://doi.org/10.1007/BF00275068