Volume 48, Number 1, January-February 2014
|Page(s)||1 - 25|
|Published online||11 October 2013|
Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points
Laboratoire de Mécanique et d’Acoustique,
CNRS, 31, chemin Joseph
Marseille Cedex 20,
Received: 1 November 2012
Revised: 31 May 2013
This study deals with the existence and uniqueness of solutions to dynamical problems of finite freedom involving unilateral contact and Coulomb friction. In the frictionless case, it has been established [P. Ballard, Arch. Rational Mech. Anal. 154 (2000) 199–274] that the existence and uniqueness of a solution to the Cauchy problem can be proved under the assumption that the data are analytic, but not if they are assumed to be only of class C∞. Some years ago, this finding was extended [P. Ballard and S. Basseville, Math. Model. Numer. Anal. 39 (2005) 59–77] to the case where Coulomb friction is included in a model problem involving a single point particle. In the present paper, the existence and uniqueness of a solution to the Cauchy problem is proved in the case of a finite collection of particles in (possibly non-linear) interactions.
Mathematics Subject Classification: 70F40 / 49J52 / 34A60
Key words: Unilateral dynamics with friction / frictional dynamical contact problems / existence and uniqueness
© EDP Sciences, SMAI, 2013
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