A simple dynamical problem involving unilateral contact and dry friction of Coulomb
type is considered as an archetype. We are concerned with the existence and uniqueness of
solutions of the system with Cauchy data. In the frictionless case, it is known
[Schatzman, Nonlinear Anal. Theory, Methods Appl.
2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class
∞. However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational Mech. Anal.
154 (2000) 199–274].
Under this analyticity hypothesis, we prove the
existence and uniqueness of solutions for the dynamical problem with unilateral contact and Coulomb
friction, extending [Ballard, Arch. Rational Mech. Anal.
154 (2000) 199–274] to the case where Coulomb friction is added to unilateral contact.