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Contribution à l'étude et à la modélisation d'un modèle de convection-diffusion dégénéré : application à l'étude du comportement migratoire des civelles dans l'estuaire de l'Adour

Abstract : The management of sea resources is one of the major stakes of the 21st century. The work described in this thesis deals with the study of the migratory behaviour of eels glass in the estuary of the Adour river. The model, which consists of a degenerated convection-diffusion partial differential equation in 2 dimensions, takes into account the influence of dynamic tide cycles (Saint Venant's system of degenerated non linear equations) and the intensity of light in the water column. First, applying the theory of topological degrees, we have showed the existence of stationnary solutions within the hydrodynamic model. Then, by injecting these solutions into our migratory model, we have established the existence of these solutions by applying the semigroups theory, the caracteristics method and J.-L. Lions theorem. Positivity and a priori estimates of biological densities have been determined beforehand. Secondly, we have proceeded to a numerical analysis. Thanks to alternate directions and the fractional steps method in a real 30-km-long area, with variable water level (actual bathymetry and influence of the tides) the results we have obtained do match, from a qualitative viewpoint, the results expected.
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https://tel.archives-ouvertes.fr/tel-00002291
Contributor : Olivier Pardo <>
Submitted on : Saturday, January 18, 2003 - 6:02:31 PM
Last modification on : Friday, January 15, 2021 - 9:24:26 AM
Long-term archiving on: : Friday, April 2, 2010 - 6:21:49 PM

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  • HAL Id : tel-00002291, version 1

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Olivier Pardo. Contribution à l'étude et à la modélisation d'un modèle de convection-diffusion dégénéré : application à l'étude du comportement migratoire des civelles dans l'estuaire de l'Adour. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2002. Français. ⟨tel-00002291⟩

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