Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations


Authors: S. Junca and M. Rascle
Journal: Quart. Appl. Math. 58 (2000), 511-521
MSC: Primary 35Q05; Secondary 35L65, 35L70, 76X05, 82D37
DOI: https://doi.org/10.1090/qam/1770652
MathSciNet review: MR1770652
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Abstract: 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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DOI: https://doi.org/10.1090/qam/1770652
Article copyright: © Copyright 2000 American Mathematical Society


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