Figure 1.
Sketch of the parts of Alexandrium catenella life we are interested in
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February
2021, 14(2): 615-633.
doi: 10.3934/dcdss.2020424
A mathematical model for marine dinoflagellates blooms
| 1. | Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LMAP, Pau, France |
| 2. | Université de Pau et des Pays de l'Adour, UPPA, CNRS, LMAP, Pau, France |
We present a model for the life cycle of a dinoflagellate in order to describe blooms. We prove the mathematical well-posedness of the model and the possibility of extinction in finite time of the alga form meaning that the full population is under the cysts from.
Keywords:
Models for algal red tide,
mathematical model in biology,
systems of non linear partial differential equations,
evolution equations,
qualitative properties.
Mathematics Subject Classification:
35K61, 35Q92, 92C80.
Citation:
M. Dambrine, B. Puig, G. Vallet. A mathematical model for marine dinoflagellates blooms. Discrete & Continuous Dynamical Systems - S,
2021, 14
(2)
: 615-633.
doi: 10.3934/dcdss.2020424
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References:
| [1] |
D. Anderson, Alexandrium fundyense cyst dynamics in the Gulf of Maine, Deep Sea Research Part Ⅱ: Topical Studies in Oceanography, 52 (2005), 2522-2542. Google Scholar |
| [2] |
F. Boyer,
Trace theorems and spatial continuity properties for the solutions of the transport equation, Differential Integral Equations, 18 (2005), 891-934.
|
| [3] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 5, Evolution problems. I, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
| [4] |
K. Flynn and D. McGillicuddy, Modelling Marine Harmful Algal Blooms: Current Status and Future Prospects, Harmful Algal Blooms: A Compendium Desk References, 3, John Wiley & Sons Ltd, 2018. Google Scholar |
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G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles Non Linéaires de L'ingénierie Pétrolière, Mathématiques & Applications (Berlin) [Mathematics & Applications], 22, Springer-Verlag, Berlin, 1996. |
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O. Guibé, A. Mokrane, Y. Tahraoui and G. Vallet, Lewy-Stampacchia's inequality for a pseudomonotone parabolic problem, Adv. Nonlinear Anal., to appear.
doi: 10.1515/anona-2020-0015. |
| [7] |
H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology, Springer Science, 2017.
doi: 10.1007/978-981-10-0188-8. |
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M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, A Pergamon Press Book, The Macmillan Co., New York, 1964. |
| [9] |
D. J. McGillicuddy, Models of harmful algal blooms: Conceptual, empirical, and numerical approaches, Journal of Marine Systems, 83 (2010), 105-105. Google Scholar |
| [10] |
H. Ruoying, D. J. McGillicuddy, B. Keafer and D. Anderson, Historic 2005 toxic bloom of Alexandrium fundyense in the western Gulf of Maine: 2. Coupled biophysical numerical modeling, Journal of Geophysical Research: Oceans, 113 (2008). Google Scholar |
show all references
References:
| [1] |
D. Anderson, Alexandrium fundyense cyst dynamics in the Gulf of Maine, Deep Sea Research Part Ⅱ: Topical Studies in Oceanography, 52 (2005), 2522-2542. Google Scholar |
| [2] |
F. Boyer,
Trace theorems and spatial continuity properties for the solutions of the transport equation, Differential Integral Equations, 18 (2005), 891-934.
|
| [3] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 5, Evolution problems. I, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
| [4] |
K. Flynn and D. McGillicuddy, Modelling Marine Harmful Algal Blooms: Current Status and Future Prospects, Harmful Algal Blooms: A Compendium Desk References, 3, John Wiley & Sons Ltd, 2018. Google Scholar |
| [5] |
G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles Non Linéaires de L'ingénierie Pétrolière, Mathématiques & Applications (Berlin) [Mathematics & Applications], 22, Springer-Verlag, Berlin, 1996. |
| [6] |
O. Guibé, A. Mokrane, Y. Tahraoui and G. Vallet, Lewy-Stampacchia's inequality for a pseudomonotone parabolic problem, Adv. Nonlinear Anal., to appear.
doi: 10.1515/anona-2020-0015. |
| [7] |
H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology, Springer Science, 2017.
doi: 10.1007/978-981-10-0188-8. |
| [8] |
M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, A Pergamon Press Book, The Macmillan Co., New York, 1964. |
| [9] |
D. J. McGillicuddy, Models of harmful algal blooms: Conceptual, empirical, and numerical approaches, Journal of Marine Systems, 83 (2010), 105-105. Google Scholar |
| [10] |
H. Ruoying, D. J. McGillicuddy, B. Keafer and D. Anderson, Historic 2005 toxic bloom of Alexandrium fundyense in the western Gulf of Maine: 2. Coupled biophysical numerical modeling, Journal of Geophysical Research: Oceans, 113 (2008). Google Scholar |
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