On multivalued solutions of one-dimensional quasilinear wave equations

The paper concerns global multivalued solutions of initial value problem for quasilinear wave equations. Besides existence and uniqueness of maximal solutions of this problem it is proved that a maximal solution possess the completeness property that is an analog of the corresponding property of ordinary differential equations. Namely, a solution of an ordinary differential equation that is defined on a maximal interval leaves any compact subset of the equation domain.