# American Institute of Mathematical Sciences

September  2008, 10(4): 887-902. doi: 10.3934/dcdsb.2008.10.887

## Analysis of a dynamic Elastic-Viscoplastic contact problem with friction

 1 Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow 2 Jagiellonian University, Faculty of Mathematics and Computer Sciences, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow 3 Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan

Received  March 2007 Revised  May 2008 Published  August 2008

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is dynamic, the material behavior is described with an elastic-viscoplastic constitutive law and the frictional contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is in the form of a system involving an integral equation coupled with an evolutionary hemivariational inequality. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract second order evolutionary inclusions with monotone operators and a fixed point theorem.
Citation: Stanislaw Migórski, Anna Ochal, Mircea Sofonea. Analysis of a dynamic Elastic-Viscoplastic contact problem with friction. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 887-902. doi: 10.3934/dcdsb.2008.10.887
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