Large times existence for thin vibrating rods

Article type: Research Article

Authors: Abels, Helmut^{; *} | Ameismeier, Tobias

Affiliations: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Correspondence: [*] Corresponding author. E-mail: [email protected].

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