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arXiv · 2109.11618

Large Times Existence for Thin Vibrating Rods

Helmut Abels·Tobias Ameismeier
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Abstract

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for arbitrarily large times, if the diameter of the cross section is chosen sufficiently small. The scaling regime is such that the limiting equations are linear.

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Helmut Abels, Tobias Ameismeier. 2021-09-23. Large Times Existence for Thin Vibrating Rods. https://arxiv.org/abs/2109.11618

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