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We investigate the weak solvability of initial boundary value problemsassociated with an ecosystem model of the marine phosphorus cycle. The analysiscovers the model equations themselves as well as their linearization which isimportant in the model calibration via parameter identification. We treat bothcases simultaneously by investigating a system of advection-diffusion-reactionequations coupled by general reaction terms and boundary conditions. We derivea weak formulation of the generalized equations and prove two theorems aboutits unique solvability provided that the reaction terms consist of Lipschitzcontinuous and monotone operators. In the proofs, we adapt different techniques(Galerkin approximation, Banach's Fixed Point Theorem) to the multi-dimensionalmodel equation. By applying the general theorems to the problems associatedwith the phosphorus model we obtain results about existence and uniqueness oftheir solutions. Actually, by assuming a generalized setting the theoremsestablish the basis for the mathematical analysis of the whole model class towhich the investigated phosphorus model belongs.

Mathematical analysis of a marine ecosystem model with nonlinear coupling terms and non-local boundary conditions