English

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}
}