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Abstract
We consider initial-boundary value problems on [0,1] associated with the integrodifferential equation of one-dimensional nonlinear viscoelasticity under the assumption X that the potential function
satisfies the growth restriction:
. For
it is shown that solutions of magnitude C∞≥0 (in a specified energy norm) can exist for all time only if
. Our results apply, in particular, to nonlinearities of the type
so that
for sufficiently large; in such a model the governing integrodifferential evolution equation may change from hyperbolic to elliptic during the course of a viscoelastic deformation.