Spectral Analysis of Integrodifferential Equations in Hilbert Spaces

Abstract

We investigate the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space and provide the spectral analysis of operator-functions describing symbols of such equations. These equations are an abstract form of linear partial integrodifferential equations arising in the viscoelasticity theory and other important applications. We establish the localization and the spectrum structure of operator-functions describing symbols of these equations.