Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 236 – 247
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0208
The Galerkin method and hinged beam dynamics
David Raske
1210 Washtenaw, Ypsilanti, MI, 48197, USA.; nonlinear.problem.solver@gmail.com
Copyright © 2023 David Raske. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 3, 2022 – Accepted: May 12, 2023 – Published: June 13, 2023
Abstract
In this paper we prove large-time existence and uniqueness of high regularity weak solutions to some initial/boundary value problems involving a nonlinear fourth order wave equation. These sorts of problems arise naturally in the study of vibrations in beams that are hinged at both ends. The method used to prove large-time existence is the Galerkin approximation method.
Keywords:
Nonlinear partial differential equations; Galerkin method; Continuum mechanics.