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

Michelle Schatzman (1)

1 UPMC - Université Pierre et Marie Curie - Paris 6

The 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.

Domaines: Mécanique des structures [physics.class-ph]

Michelle Schatzman. A hyperbolic problem of second order with unilateral constraints: The vibrating string with a concave obstacle. Journal of Mathematical Analysis and Applications, 1980, 73 (1), pp.138-191. ⟨10.1016/0022-247X(80)90026-8⟩. ⟨hal-01620859⟩