Open AccessCorrect solvability and representation of the solutions of Volterra integro-differential equations with exponential-fractional kernels
Author(s) -
В. В. Власов,
Н. А. Раутиан
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524885476-480
Subject(s) - mathematics , hilbert space , exponential function , operator (biology) , mathematical analysis , differential equation , c0 semigroup , series (stratigraphy) , volterra integral equation , representation (politics) , integral equation , paleontology , biochemistry , chemistry , repressor , biology , transcription factor , gene , politics , political science , law
For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.