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Theses

Homogénéisation de lois de conservation scalaires et d'équations de transport

Abstract : In this thesis, we study the asymptotic behavior of solutions of a class of partial differential equations with strongly oscillating coefficients. First, we focus on a family of nonlinear evolution equations, namely parabolic scalar conservation laws. These equations are encountered in various problems of fluid mechanics and nonlinear electromagnetism. The flux is assumed to be periodic with respect to the space variable, and the period of the oscillations goes to zero. The asymptotic profiles in the microscopic and macroscopic variables are first identified. Then, we prove a result of strong convergence; in particular, when the initial data does not match the microscopic outline dictated by the equation, it is shown that there is an initial layer in time during which the solution adapts itself to this profile. The other equation studied in this thesis is a linear transport equation, modeling the evolution of the density of charged particles in a highly oscillating random electric potential. It is proved that the density has fast oscillations in time and space, as a response to the excitation by the electric potential. We also derive explicit formulas for the homogenized transport operator when the space dimension is equal to one.
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https://tel.archives-ouvertes.fr/tel-00182850
Contributor : Anne-Laure Dalibard <>
Submitted on : Monday, October 29, 2007 - 11:31:44 AM
Last modification on : Wednesday, September 23, 2020 - 4:28:32 AM
Long-term archiving on: : Monday, September 24, 2012 - 2:46:35 PM

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  • HAL Id : tel-00182850, version 1

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Anne-Laure Dalibard. Homogénéisation de lois de conservation scalaires et d'équations de transport. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2007. Français. ⟨tel-00182850⟩

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