Mathematical Problems in Engineering
Volume 2005 (2005), Issue 4, Pages 437-453

Maximal monotone model with delay term of convolution

Claude-Henri Lamarque,1 Jérôme Bastien,2 and Matthieu Holland3

1Laboratoire Géomatériaux, Département Génie Civil et Bâtiment, URA 1652 CNRS, École Nationale des Travaux Publics de l'Etat, rue Maurice-Audin, Vaulx-en-Velin Cedex 69518, France
2Laboratoire Mécatronique 3M, Équipe d'accueil A 3318, Université de Technologie de Belfort-Montbéliard, Belfort Cedex 90010, France
3CETE Normandie Centre, Grand-Quevilly Cedex 76121, France

Received 10 February 2004

Copyright © 2005 Claude-Henri Lamarque et al. 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.


Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics) or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description) with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction), we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given.