From the Newton equation to the wave equation in some simple cases
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CEA, DAM, DIF, F-91297, Arpajon
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École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2
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Collège de France, 11, place Marcelin Berthelot, 75231 Paris Cedex 05
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Received:
01 September 2011
Revised:
01 January 2012
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Primary: 35Q35, 35Q72, 82C21; Secondary: 35L70, 70F45, 82C22.
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We prove that, in some simple situations at least, the one-dimensional wave equation is
the limit as the microscopic scale goes to zero of some time-dependent
Newton type equation of motion for atomistic systems. We address both
some linear and some nonlinear cases.
Citation: Xavier Blanc, Claude Le Bris, Pierre-Louis Lions. From the Newton equation to the wave equation in some simple cases[J]. Networks and Heterogeneous Media, 2012, 7(1): 1-41. doi: 10.3934/nhm.2012.7.1
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Abstract
We prove that, in some simple situations at least, the one-dimensional wave equation is
the limit as the microscopic scale goes to zero of some time-dependent
Newton type equation of motion for atomistic systems. We address both
some linear and some nonlinear cases.
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