Well-Posedness and Spectral Analysis of Volterra Integro-Differential Equations with Singular Kernels

Integro-differential equations with unbounded operator coefficients in a Hilbert space are considered. Such equations arise in viscoelasticity theory, thermal physics, and homogenization problems in multiphase media. Initial–boundary value problems for the indicated equations are proved to be well posed, and their spectral analysis is performed.