Solutions to a degenerate system of parabolic equations from marine biology

A system of parabolic and ordinary differential equations ut = a2 uxx + F(u,v,w), vt = a2 vxx + G(u,v,w), wx = -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.