Electron. J. Diff. Eqns., Vol. 2004(2004), No. 83, pp. 1-21.

Dynamic contact with Signorini's condition and slip rate dependent friction

Kenneth Kuttler, Meir Shillor

Existence of a weak solution for the problem of dynamic frictional contact between a viscoelastic body and a rigid foundation is established. Contact is modelled with the Signorini condition. Friction is described by a slip rate dependent friction coefficient and a nonlocal and regularized contact stress. The existence in the case of a friction coefficient that is a graph, which describes the jump from static to dynamic friction, is established, too. The proofs employ the theory of set-valued pseudomonotone operators applied to approximate problems and a priori estimates.

Submitted October 15, 2003. Published June 11, 2004.
Math Subject Classifications: 74M10, 35Q80, 49J40, 74A55, 74H20, 74M15.
Key Words: Dynamic contact, Signorini condition, slip rate dependent friction, nonlocal friction, viscoelastic body, existence.

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Kenneth Kuttler
Department of Mathematics
Brigham Young University
Provo, UT 84602, USA
email: klkuttle@math.byu.edu
Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: shillor@oakland.edu

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