Solvability and spectral analysis of integro-differential equations arising in the theory of heat transfer and acoustics (Q630225)

The authors study integro-differential equations with unbounded operator coefficients in a Hilbert space. The solvability of the initial-boundary value problems for these equations is established in weighted Sobolev spaces. The spectrum of the abstract Gurtin-Pipkin integro-differential equation is studied. The main attention is paid to spectral questions and to the asymptotic behavior of solutions to evolution equations and their images under the time Laplace transform.