Nonlinear waves in adhesive strings
  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. 
Giuseppe Maria Coclite, Giuseppe Florio, Marilena Ligabo', Francesco   Maddalena
math.AP math-ph math.MP