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

## 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 |

### Actions (login required)

View Item |