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From the Newton Equation to the Wave Equation: The Case of Shock Waves

From the Newton Equation to the Wave Equation: The Case of Shock Waves AbstractWe study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, and Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show numerically and mathematically that if the distances between particles remain bounded, it is not the case any more when there are shocks at least for a convex nearest-neighbor interaction potential with convex derivative. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics Research Express Oxford University Press

From the Newton Equation to the Wave Equation: The Case of Shock Waves

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References (37)

Publisher
Oxford University Press
Copyright
© The Author(s) 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
ISSN
1687-1200
eISSN
1687-1197
DOI
10.1093/amrx/abx001
Publisher site
See Article on Publisher Site

Abstract

AbstractWe study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, and Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show numerically and mathematically that if the distances between particles remain bounded, it is not the case any more when there are shocks at least for a convex nearest-neighbor interaction potential with convex derivative.

Journal

Applied Mathematics Research ExpressOxford University Press

Published: Sep 1, 2017

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