Within the theory of linear viscoelasticity, we seek solutions to the inversion problem of the constitutive equation respectively in L(2) and in the space S' of the tempered distributions. Successively we study the quasi-static problem in S'. 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. References: 19
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