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frictional dynamical contact problems

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points
Alexandre Charles, Patrick Ballard
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 1 / January 2014

Published online by Cambridge University Press:

11 October 2013, pp. 1-25

Print publication:

January 2014
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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.