Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string

Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems with a localized term and show its well-posedness in weighted Sobolev spaces. We then consider the linearized system for the motion of an inextensible hanging string. Well-posedness of its initial boundary value problem is demonstrated as an application of the result obtained in the first part.