Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points

Charles, Alexandre; Ballard, Patrick

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 1-25

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.

Classification : 70F40, 49J52, 34A60
Keywords: unilateral dynamics with friction, frictional dynamical contact problems, existence and uniqueness

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