From the Newton equation to the wave equation in some simple cases | Zendy

Xavier Blanc | Zendy; Claude Le Bris | Zendy; PierreLouis Lions | Zendy

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From the Newton equation to the wave equation in some simple cases

Author(s) -

Xavier Blanc,

Claude Le Bris,

PierreLouis Lions

Publication year - 2012

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2012.7.1

Subject(s) - simple (philosophy) , limit (mathematics) , wave equation , mathematical analysis , zero (linguistics) , nonlinear system , mathematics , wave motion , burgers' equation , scale (ratio) , physics , classical mechanics , partial differential equation , mechanics , quantum mechanics , philosophy , linguistics , epistemology

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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