This article is cited in 6 papers

Investigation of operator models arising in viscoelasticity theory

V. V. Vlasov, N. A. Rautian

Lomonosov Moscow State University, Moscow, Russia

Abstract: We study the correct solvability of initial problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space. We do spectral analysis of operator-functions that are symbols of such equations. The equations under consideration are an abstract form of linear integrodifferential equations with partial derivatives arising in viscoelasticity theory and having a number of other important applications. We describe localization and structure of the spectrum of operatorfunctions that are symbols of such equations.

UDC: 517.968.72

DOI: 10.22363/2413-3639-2018-64-1-60-73