Nontrivial Periodic Solutions of Marine Ecosystem Models of N-DOP type

Roschat, Christina and Slawig, Thomas (2014) Nontrivial Periodic Solutions of Marine Ecosystem Models of N-DOP type arXiv e-prints . arXiv: 1409.7540.

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Abstract

We investigate marine ecosystem models of N-DOP type with regard to nontrivial periodic solutions. The elements of this important, widely-used model class typically consist of two coupled advection-diffusion-reaction equations. The corresponding reaction terms are divided into a linear part, describing the transformation of one model variable into the other, and a bounded nonlinear part. Additionally, the model equations conserve the mass contained in the system, i.e. the masses of both variables add up to a constant total mass. In particular, the trivial function is a periodic solution. In this paper, we prove that there is at least one periodic solution for every prescribed total mass. The proof makes use of the typical properties of N-DOP type models by combining results from monotone operator theory and a fixed point argument. In the end, we apply the theorem to the PO4-DOP model, an N-DOP type model which is well-known and often used.

Document Type: Article
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Projects: Future Ocean
Date Deposited: 27 Aug 2019 09:51
Last Modified: 27 Aug 2019 09:51
URI: http://eprints.uni-kiel.de/id/eprint/47585

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