Journal of Applied Mathematics

Journal of Applied Mathematics / 2002 / Article

Open Access

Volume 2 |Article ID 350590 | https://doi.org/10.1155/S1110757X02000219

Mikäel Barboteu, Weimin Han, Mircea Sofonea, "A frictionless contact problem for viscoelastic materials", Journal of Applied Mathematics, vol. 2, Article ID 350590, 21 pages, 2002. https://doi.org/10.1155/S1110757X02000219

A frictionless contact problem for viscoelastic materials

Received12 Mar 2001
Revised04 Sep 2001

Abstract

We consider a mathematical model which describes the contact between a deformable body and an obstacle, the so-called foundation. The body is assumed to have a viscoelastic behavior that we model with the Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the well-known Signorini condition in a form with a zero gap function. We present two alternative yet equivalent weak formulations of the problem and establish existence and uniqueness results for both formulations. The proofs are based on a general result on evolution equations with maximal monotone operators. We then study a semi-discrete numerical scheme for the problem, in terms of displacements. The numerical scheme has a unique solution. We show the convergence of the scheme under the basic solution regularity. Under appropriate regularity assumptions on the solution, we also provide optimal order error estimates.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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