Uniqueness and continuous dependence on data for one-dimensional impact problems

One dimensional dynamics with impact are described by the data of a closed interval K, a function f of time, position, and velocity, and a restitution coefficient e ∈ [0,1). When u is in the interior of K, it satisfies the ordinary differential equation ü = f(t, u, ü). When it hits the end points of K, the velocity is reversed and multiplied by e. If f is analytic with respect to its three arguments, it is proved that uniqueness holds for the forward Cauchy problem.