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REVIEW ARTICLES

Initial Value Problems in Viscoelasticity

[+] Author and Article Information
W. J. Hrusa

Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

J. A. Nohel

Center for the Mathematical Sciences, University of Wisconsin-Madison, Madison, WI 53705

M. Renardy

Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-4097

Appl. Mech. Rev 41(10), 371-378 (Oct 01, 1988) (8 pages) doi:10.1115/1.3151871 History: Online June 03, 2009

Abstract

We review some recent mathematical results concerning integrodiff erential equations that model the motion of one-dimensional nonlinear viscoelastic materials. In particular, we discuss global (in time) existence and long-time behavior of classical solutions, as well as the formation of singularities in finite time from smooth initial data. Although the mathematical theory is comparatively incomplete, we make some remarks concerning the existence of weak solutions (i e, solutions with shocks). Some relevant results from linear wave propagation will also be discussed.

Copyright © 1988 by American Society of Mechanical Engineers
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