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* . When , 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 .

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DOI:
https://doi.org/10.1090/qam/1770652

Article copyright:
© Copyright 2000
American Mathematical Society