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

Alexandre Charles; Patrick Ballard

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

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

Abstract

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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.

How to cite

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Charles, 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 -

References

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  13. [13] D. Percivale, Uniqueness in the Elastic Bounce Problem, I, J. Diff. Eqs.56 (1985) 206–215. Zbl0521.73006MR774163
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