Nonlinear waves in adhesive strings
Analysis of PDEs
2016-03-25 v1 Mathematical Physics
math.MP
Abstract
We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state, beyond such a value the stress discontinuously drops to zero. Therefore the semilinear equation is characterized by a source term presenting jump discontinuity. Well-posedness of the initial boundary value problem of Neumann type, as well as qualitative properties of the solutions are studied and the evolution of different initial conditions are numerically investigated.
Cite
@article{arxiv.1603.07648,
title = {Nonlinear waves in adhesive strings},
author = {Giuseppe Maria Coclite and Giuseppe Florio and Marilena Ligabo' and Francesco Maddalena},
journal= {arXiv preprint arXiv:1603.07648},
year = {2016}
}