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

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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.
    Mathematics Subject Classification: Primary: 35Q35, 35Q72, 82C21; Secondary: 35L70, 70F45, 82C22.


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