Spectral analysis of Volterra integrodifferential equations with the kernels, depending on parameter

Romeo Perez Ortiz; Victor V. Vlasov; Nadezhda A. Rautian

paper

Spectral analysis of Volterra integrodifferential equations with the kernels, depending on parameter

arXiv:1710.07112

Abstract

Spectral analysis of operator-functions which are the symbols of the abstract integrodifferential equations of the Gurtin-Pipkin is provided. These equations represent abstract wave equations disturbed by terms involving Volterra operators. Correct solvability in the Sobolev space $W_{2}^{2} ((0, T), A^{2})$ , for arbitrary $T > 0$ , of that abstract integrodifferential equations is also studied.