On the Properties of a Semigroup of Operators Generated by a Volterra Integro-Differential Equation Arising in the Theory of Viscoelasticity.

Without taking into account external friction, small transverse vibrations of a viscoelastic pipeline of unit length are described for nonnegative values of time in dimensionless variables by an integro-differential equation with hinged conditions at the ends and with initial conditions. The solution of this equation can be written in terms of an operator semigroup. In the present paper, we establish that this equation generates a semigroup that is analytic in some sector of the right half-plane. [ABSTRACT FROM AUTHOR]