Abstract
Abstract : It is shown that the evolution of the electric displacement field in a simple class of holohedral isotropic dielectrics can be modeled by an initial value problem associated with a certain (damped) linear integrodifferential equation in Hilbert space. By employing logarithmic convexity arguments growth estimates are derived for solutions of this integrodifferential equation which lie in uniformly bounded subsets of the appropriate Hilbert space; the results yield both upper and lower bounds for the magnitude of the electric displacement field in the class of isotropic holohedral dielectrics which is modeled by the abstract initial-value problem.
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