Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points. (11th October 2013)

• Record Type: Journal Article
• Authors: Charles, Alexandre; Ballard, Patrick
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 1(2013)
• Page Start: 1
• Page End: 25
• Publication Date: 2013-10-11
• Subjects: Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2013092
• Languages: English
• ISSNs: 0764-583X

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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, <italic>Arch. Rational Mech. Anal. </italic><bold>154 </bold>(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 <italic>C</italic>^∞. Some years ago, this finding was extended [P. Ballard and S. Basseville, <italic>Math. Model. Numer. Anal. </italic><bold>39 </bold>(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.</p> </abstract>