  We investigate the weak solvability of initial boundary value problems
associated with an ecosystem model of the marine phosphorus cycle. The analysis
covers the model equations themselves as well as their linearization which is
important in the model calibration via parameter identification. We treat both
cases simultaneously by investigating a system of advection-diffusion-reaction
equations coupled by general reaction terms and boundary conditions. We derive
a weak formulation of the generalized equations and prove two theorems about
its unique solvability provided that the reaction terms consist of Lipschitz
continuous and monotone operators. In the proofs, we adapt different techniques
(Galerkin approximation, Banach's Fixed Point Theorem) to the multi-dimensional
model equation. By applying the general theorems to the problems associated
with the phosphorus model we obtain results about existence and uniqueness of
their solutions. Actually, by assuming a generalized setting the theorems
establish the basis for the mathematical analysis of the whole model class to
which the investigated phosphorus model belongs.
