A hyperbolic problem of second order with unilateral constraints: The vibrating string with a concave obstacle

AbstractThe motion of a vibrating string constrained to remain above a material concave obstacle is studied. It is assumed that the string does not lose energy when it hits the obstacle. A set of natural inequations describes this model; an energy condition in an ad hoc form must be added to ensure uniqueness. Existence and uniqueness are proved for the Cauchy problem; the case of an infinite string and the case of a finite string with fixed ends are considered