Solutions to a degenerate system of parabolic equations from marine biology

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.