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Article Dans Une Revue Quarterly of Applied Mathematics Année : 2000

Relaxation of the isothermal Euler-Poisson system to the Drift-Diffusion equations

Résumé

We consider the one-dimensional Euler-Poisson system in the isothermal case, with a friction coefficient $ {\varepsilon ^{ - 1}}$. When $ \varepsilon \to {0_ + }$, we show that the sequence of entropy-admissible weak solutions constructed in [PRV] converges to the solution to the drift-diffusion equations. We use the scaling introduced in [MN2], who proved a quite similar result in the isentropic case, using the theory of compensated compactness. On the one hand, this theory cannot be used in our case; on the other hand, exploiting the linear pressure law, we can give here a much simpler proof by only using the entropy inequality and de la Vallée-Poussin criterion of weak compactness in $ {L^{1}}$.
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Dates et versions

hal-01312342 , version 1 (05-05-2016)

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Stéphane Junca, Michel Rascle. Relaxation of the isothermal Euler-Poisson system to the Drift-Diffusion equations. Quarterly of Applied Mathematics, 2000, 58 (3), pp.511-521. ⟨10.1090/qam/1770652⟩. ⟨hal-01312342⟩
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