Abstract
Employing a modified version of a concavity argument for abstract differential equations, we obtain growth estimates for solutions to a class of initial-value problems associated with an undamped linear integrodifferential equation in Hilbert space. Our results are applied to the derivation of growth estimates for the gradients of electric displacement fields occurring in rigid nonconducting material dielectrics of Maxwell-Hopkinson type and these, in turn, are used to bound constitutive constants appearing in theories associated with such material response.
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