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Journal of Function Spaces and Applications
Volume 3 (2005), Issue 3, Pages 251-262
http://dx.doi.org/10.1155/2005/379248

Infinite-dimensional projected dynamics and the 1-dimensional obstacle problem

Department of Mathematics and Statistics, MacNaughton Hall, Room 548, University of Guelph, Guelph, Ontario, Canada

Received 1 September 2004

Academic Editor: Lars-Erik Persson

Copyright © 2005 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.

Abstract

In this paper we present a direct application of the theory of infinite-dimensional projected dynamical systems (PDS) related to the well-known obstacle problem, i.e., the problem of determining the shape of an elastic string stretched over a body (obstacle). While the obstacle problem is static in nature and is solved via variational inequalities theory, we show here that the dynamic problem of describing the vibration movement of the string around the obstacle is solved via the infinite-dimensional theory of projected dynamical systems.