Stability and Well-posedness of a Nonlinear Railway Track Model
Analysis of PDEs
2018-07-04 v2
Abstract
Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in presence of an input. With the aid of a suitable Lyapunov function, existence and exponential stability of classical solutions is established for certain inputs. The Lyapunov function is further used to find an a-priori estimate of the solutions, and also to study the input-to-state stability (ISS) of mild solutions.
Keywords
Cite
@article{arxiv.1803.02938,
title = {Stability and Well-posedness of a Nonlinear Railway Track Model},
author = {M. Sajjad Edalatzadeh and Kirsten A. Morris},
journal= {arXiv preprint arXiv:1803.02938},
year = {2018}
}