Properties of solutions of integro-differential equations arising in heat and mass transfer theory

Abstract

. The aim of the present paper is to study the asymptotic behavior of solutions of integro-differential equations on the basis of spectral analysis of their symbols. To this end, we obtain representations of strong solutions of these equations in the form of a sum of terms corresponding to the real and nonreal parts of the spectrum of the operator functions that are the symbols of these equations. These representations are new for the class of integro-differential equations considered in the paper.