  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.
