Abstract
Within the theory of linear viscoelasticity, we seek solutions to the inversion problem of the constitutive equation respectively inL 2 and in the spaceS′ of the tempered distributions. Successively we study the quasi-static problem inS′. Both problems admit one and only one solution if the relaxation function satisfies Graffi's inequality. Finally we show that the inversion problem and the quasi-static one are deeply connected and that every counterexample about the existence or uniqueness of the solutions for the first problem also provides a counterexample for the latter.
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