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The dynamic problem in linear viscoelasticity: Uniqueness for unbounded solutions in the past. (Italian. English summary) Zbl 0678.73037
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 [M. E. Gurtin and 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.
MSC:
74Hxx Dynamical problems in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
45N05 Abstract integral equations, integral equations in abstract spaces
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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References:
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