Open AccessInvestigation of Integrodifferential Equations by Methods of Spectral Theory
Author(s) -
В. В. Власов,
Н. А. Раутиан
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-2-255-284
Subject(s) - hilbert space , operator (biology) , mathematics , mathematical analysis , spectral theory , partial differential equation , viscoelasticity , simultaneous equations , differential equation , physics , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
This paper provides a survey of results devoted to the study of integrodifferential equations with unbounded operator coefficients in a Hilbert space. These equations are operator models of integrodifferential partial differential equations arising in numerous applications: in the theory of viscoelasticity, in the theory of heat propagation in media with memory (Gurtin-Pipkin equations), and averaging theory. The most interesting and profound results of the survey are devoted to the spectral analysis of operator functions that are symbols of the integrodifferential equations under study.