Study of functional-differential equations with unbounded operator coefficients (Q1707161)

The authors present a survey study of functional-differential and integro-differential equations where the principal part is an abstract hyperbolic equation, while the perturbed part incorporates unbounded variable operator coefficients with variable delays. Moreover, they consider integro-differential equations with parameter-dependent kernels which have applications to viscoelasticity, diffusion and heat conduction in media with memory. Several theorems on well-posedness and spectral analysis are given. The proofs of the theorems are omitted. The authors give a reference to their previously published results.