A Dynamic Frictional Contact Problem with Normal Damped Response |
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Authors: | O Chau W Han M Sofonea |
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Institution: | (1) Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France;(2) Department of Mathematics, University of Iowa, Iowa City, IA, 52242, U.S.A. |
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Abstract: | We consider a mathematical model which describes the frictional contact between a viscoelastic body and a reactive foundation. The process is assumed to be dynamic and the contact is modeled with a general normal damped response condition and a local friction law. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution, using results on evolution equations with monotone operators and a fixed point argument. We then introduce and study a fully discrete numerical approximation scheme of the variational problem, in terms of the velocity variable. The numerical scheme has a unique solution. We derive error estimates under additional regularity assumptions on the data and the solution. |
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Keywords: | viscoelastic material frictional contact normal damped response weak solution numerical approximation error estimates |
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