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

Alexandre Charles; Patrick Ballard

- Volume: 48, Issue: 1, page 1-25
- ISSN: 0764-583X

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topCharles, Alexandre, and 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 48.1 (2014): 1-25. <http://eudml.org/doc/273150>.

@article{Charles2014,

abstract = {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.},

author = {Charles, Alexandre, Ballard, Patrick},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {unilateral dynamics with friction; frictional dynamical contact problems; existence and uniqueness},

language = {eng},

number = {1},

pages = {1-25},

publisher = {EDP-Sciences},

title = {Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points},

url = {http://eudml.org/doc/273150},

volume = {48},

year = {2014},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 1

SP - 1

EP - 25

AB - 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.

LA - eng

KW - unilateral dynamics with friction; frictional dynamical contact problems; existence and uniqueness

UR - http://eudml.org/doc/273150

ER -

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