UNIQUENESS AND CONTINUOUS DEPENDENCE ON DATA FOR ONE-DIMENSIONAL IMPACT PROBLEMS

One dimensional dynamics with impact are described by the data of a cl osed interval K, a function f of time, position, and velocity, and a r estitution coefficient e is an element of [0, 1). When u is in the int erior of K, it satisfies the ordinary differential equation (u)double over dot = f(t, u, (u) over dot). When it hits the end points of K, th e velocity is reversed and multiplied by e. If f is analytic with resp ect to its three arguments, it is proved that uniqueness holds for the forward Cauchy problem. (C) 1998 Elsevier Science Ltd. All rights res erved.