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Article type: Research Article
Authors: Abels, Helmut; * | Ameismeier, Tobias
Affiliations: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Correspondence: [*] Corresponding author. E-mail: helmut.abels@mathematik.uni-regensburg.de.
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.
Keywords: Wave equation, von Kármán equation, nonlinear elasticity, long time existence
DOI: 10.3233/ASY-221778
Journal: Asymptotic Analysis, vol. 131, no. 3-4, pp. 471-512, 2023
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