On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity


The asymptotic behaviour of a scalar linear nonconvolution Volterra equation is investigated; the equation is that satisfied by the modes of a viscoelastic rod bending quasi-statically. A sufficient condition for the trivial solution to be asymptotic stable is given, as well as results on describing the exact rate of decay: in the case that the trivial solution is unstable, the exact rate of growth of solutions is specified.

DOI Code: 10.1285/i15900932v27n2p215

Linear viscoelasticity; Resolvent; Renewal equation; Laplace transform

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