The dynamic problem in linear viscoelasticity: Uniqueness for unbounded solutions in the past (Q1124414)

Summary: We prove that the dynamic problem in linear viscoelasticity has a unique weak solution in a class of unbounded functions for \(t\to -\infty\). We assume, for the relaxation function of the material, the dissipativity condition considered by Gurtin-Herrera [\textit{M. E. Gurtin} and \textit{I. Herrera}, Q. Appl. Mat. 23, 235-245 (1965; Zbl 0173.527)] and we require the instantaneous elastic modulus to be greater than a value depending on the dissipativity condition, on the memory of the material and on the asymptotic behaviour in the past of the admissible eigensolutions.