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Existence of solutions and asymptotic limits of the Euler-Poisson and the quantum drift-diffusion systems. Applications to semiconductors and plasmas.

Abstract : This thesis is devoted to two different systems of equations used in the mathematical modeling of semiconductors and plasmas.
In a first part, we consider a fluid-dynamical model called the Euler-Poisson system. Using an asymptotic expansion method, we study the limit to zero of the three physical parameters which arise in this system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates.
In a second part, we consider the quantum drift-diffusion model. First, we show the existence of solutions (for a general doping profile) and the quasineutral limit (for a vanishing doping profile), for the transient bipolar model in one-space dimension. Then we prove some new regularity properties for the solutions of the equation obtained in the quasineutral limit. These new properties allow us to also show the positivity of solutions to this equation for times large enough.
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https://tel.archives-ouvertes.fr/tel-00120583
Contributor : Ingrid Violet <>
Submitted on : Friday, December 15, 2006 - 3:11:09 PM
Last modification on : Thursday, February 25, 2021 - 10:34:02 AM
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  • HAL Id : tel-00120583, version 1

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Ingrid Violet. Existence of solutions and asymptotic limits of the Euler-Poisson and the quantum drift-diffusion systems. Applications to semiconductors and plasmas.. Mathematics [math]. Université Blaise Pascal - Clermont-Ferrand II, 2006. English. ⟨tel-00120583⟩

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