Initial layers and zero‐relaxation limits of multidimensional Euler–Poisson equations |
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Authors: | Mohamed‐Lasmer Hajjej Yue‐Jun Peng |
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Institution: | 1. Clermont Université, Université Blaise Pascal, , 63000 Clermont‐Ferrand, France;2. Laboratoire de Mathématiques, CNRS‐UMR 6620, Complexe scientifique Les Cézeaux, , 63171 Aubière cedex, France |
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Abstract: | In this paper, we consider zero‐relaxation limits for periodic smooth solutions of the time‐dependent Euler–Poisson system. For well‐prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill‐prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in a time interval independent of the relaxation time, and their convergence is justified by establishing uniform energy estimates. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | Euler– Poisson equations drift– diffusion equations zero‐relaxation limit initial layer correction |
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