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.

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