Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, p. 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.

DOI : https://doi.org/10.1051/m2an/2013092
Classification:  70F40,  49J52,  34A60
Keywords: unilateral dynamics with friction, frictional dynamical contact problems, existence and uniqueness
@article{M2AN_2014__48_1_1_0,
     author = {Charles, Alexandre and Ballard, Patrick},
     title = {Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {1},
     year = {2014},
     pages = {1-25},
     doi = {10.1051/m2an/2013092},
     mrnumber = {3177835},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_1_1_0}
}
Charles, Alexandre; Ballard, Patrick. Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, pp. 1-25. doi : 10.1051/m2an/2013092. http://www.numdam.org/item/M2AN_2014__48_1_1_0/

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