Well-Posed Solvability of Volterra Integro-Differential Equations Arising in Viscoelasticity Theory

We discuss the well-posed solvability and exponential stability of solutions of abstractintegro-differential equations where the kernels of integral operators are of general type and lie inthe space of functions integrable on the positive half-line. The abstract integro-differentialequations studied in the present paper are operator models of viscoelasticity theory problems. Theproposed approach to the study of these integro-differential equations is related to an applicationof semigroup theory and can also be used to study other integro-differential equations containingintegral terms of the Volterra convolution type.