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Asymptotic models in oceanography Description

Key Elements

Code

MEDP 506

Formation

M2 Partial Differential Equations and Numerical Analysis

Semester

1

Credits

4

Number of Teaching Hours

28

Number of Tutoring Sessions

0

Number of Laboratory Sessions

0

Content

Objective

Content

Part I: The aim of this course, in the first part, is to introduce the notion of hyperbolicity in PDE’s problems and the methods to study hyperbolic systems. We study the method of characteristics, the notion of hyperbolicity, linear and quasi-linear systems (case of symmetrizable systems) by the energy estimation method (in particular we introduce during this method the Gagliardo-Niremberg and Moser inequalities and the Kato-Ponce commutator estimates). Part II: The second part is concerned with the mathematical study of asymptotic models obtained from the water waves system by "zooming" at different regimes of wavelengths, amplitudes,... One obtains by this process many clasical equations or systems : Boussinesq, Saint-Venant… We will present various results on the Cauchy problem for those models, trying to keep in mind their physical origin.