Nonstationary motion of an inextensible hanging string

We consider the motion of an inextensible hanging string of finite length under the action of the gravity. The motion is governed by nonlinear and nonlocal hyperbolic equations, which is degenerate at the free end of the string. We report that the initial boundary value problem to the equations of motion is well-posed locally in time in weighted Sobolev spaces at the quasilinear regularity threshold under a stability condition. This is a joint work with Masahiro Takayama at Keio University.