  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.
