Existence and uniqueness for dynamical unilateral contact with Coulomb friction : a model problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 1, p. 59-77

A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl. 2 (1978) 355-373] that pathologies of non-uniqueness can exist, even if all the data are of class ${C}^{\infty }$. However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational Mech. Anal. 154 (2000) 199-274]. Under this analyticity hypothesis, we prove the existence and uniqueness of solutions for the dynamical problem with unilateral contact and Coulomb friction, extending [Ballard, Arch. Rational Mech. Anal. 154 (2000) 199-274] to the case where Coulomb friction is added to unilateral contact.

DOI : https://doi.org/10.1051/m2an:2005004
Classification:  34A60,  49J52,  70F40
Keywords: unilateral dynamics with friction, existence and uniqueness
@article{M2AN_2005__39_1_59_0,
author = {Ballard, Patrick and Basseville, St\'ephanie},
title = {Existence and uniqueness for dynamical unilateral contact with Coulomb friction : a model problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {39},
number = {1},
year = {2005},
pages = {59-77},
doi = {10.1051/m2an:2005004},
zbl = {1089.34010},
mrnumber = {2136200},
language = {en},
url = {http://www.numdam.org/item/M2AN_2005__39_1_59_0}
}

Ballard, Patrick; Basseville, Stéphanie. Existence and uniqueness for dynamical unilateral contact with Coulomb friction : a model problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 1, pp. 59-77. doi : 10.1051/m2an:2005004. http://www.numdam.org/item/M2AN_2005__39_1_59_0/

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