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.
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 },
pages = {1--25},
year = {2014},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
doi = {10.1051/m2an/2013092},
mrnumber = {3177835},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013092/}
}
TY - JOUR AU - Charles, Alexandre AU - Ballard, Patrick TI - Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1 EP - 25 VL - 48 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013092/ DO - 10.1051/m2an/2013092 LA - en ID - M2AN_2014__48_1_1_0 ER -
%0 Journal Article %A Charles, Alexandre %A Ballard, Patrick %T Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1-25 %V 48 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013092/ %R 10.1051/m2an/2013092 %G en %F 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 , Tome 48 (2014) no. 1, pp. 1-25. doi: 10.1051/m2an/2013092
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