[PDF][PDF] From the Newton equation to the wave equation: the case of shock waves
X Blanc, M Josien - Applied Mathematics Research eXpress, 2017 - academic.oup.com
X Blanc, M Josien
Applied Mathematics Research eXpress, 2017•academic.oup.comWe 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.
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.
Abstract
We 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.
Oxford University Press