# American Institute of Mathematical Sciences

December  2011, 31(4): 1039-1051. doi: 10.3934/dcds.2011.31.1039

## On some frictional contact problems with velocity condition for elastic and visco-elastic materials

 1 University of La Réunion, PIMENT EA4518, 97715 Saint-Denis Messag cedex 9 La Réunion, France, France, France

Received  October 2009 Revised  May 2010 Published  September 2011

We study the evolution of a class of quasistatic problems, which describe frictional contact between a body and a foundation. The constitutive law of the materials is elastic, or visco-elastic: with short or long memory, and the contact is modelled by a general subdifferential condition on the velocity. We derive weak formulations for the models and establish existence and uniqueness results. The proofs are based on evolution variational inequalities, in the framework of monotone operators and $fi$xed point methods. We show the approach of the viscoelastic solutions to the corresponding elastic solutions, when the viscosity tends to zero. Finally we also study the approach to short memory visco-elasticity when the long memory relaxation coefficients vanish.
Citation: Khalid Addi, Oanh Chau, Daniel Goeleven. On some frictional contact problems with velocity condition for elastic and visco-elastic materials. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1039-1051. doi: 10.3934/dcds.2011.31.1039
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##### References:
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