Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem
Laboratoire de Mécanique et d'Acoustique, 31, Chemin Joseph
Aiguier, 13402 Marseille Cedex 20, France. email@example.com
Revised: 4 November 2004
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 C∞. 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.
Mathematics Subject Classification: 34A60 / 49J52 / 70F40
Key words: Unilateral dynamics with friction / existence and uniqueness.
© EDP Sciences, SMAI, 2005