Regularity and energy transfer for a nonlinear beam equation
Analysis of PDEs
2021-02-01 v1 Mathematical Physics
math.MP
Abstract
In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral decomposition method we show that the main effects induced by the nonlinearity at the transition from attached to detached states can be traced in a loss of regularity of the solution and in a migration of the total energy through the scales.
Cite
@article{arxiv.2011.05246,
title = {Regularity and energy transfer for a nonlinear beam equation},
author = {Giuseppe Maria Coclite and Giuseppe Fanizza and Francesco Maddalena},
journal= {arXiv preprint arXiv:2011.05246},
year = {2021}
}
Comments
6 pages