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Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem

Published online by Cambridge University Press:  15 March 2005

Patrick Ballard  and
Stéphanie Basseville
Patrick Ballard
Affiliation:
Laboratoire de Mécanique et d'Acoustique, 31, Chemin Joseph Aiguier, 13402 Marseille Cedex 20, France. ballard@lma.cnrs-mrs.fr
Stéphanie Basseville
Affiliation:
Laboratoire de Mécanique et d'Acoustique, 31, Chemin Joseph Aiguier, 13402 Marseille Cedex 20, France. ballard@lma.cnrs-mrs.fr
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Abstract

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 ∞. 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 theexistence 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.

Keywords

Unilateral dynamics with frictionexistence and uniqueness.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 1 , January 2005 , pp. 59 - 77
Copyright
© EDP Sciences, SMAI, 2005

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References

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