Open AccessSemigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals
Author(s) -
В. В. Власов,
В. В. Власов,
Н. А. Раутиан,
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 - 10.22363/2413-3639-2021-67-3-507-525
Subject(s) - mathematics , semigroup , differential equation , hilbert space , cauchy problem , integro differential equation , mathematical analysis , riemann–stieltjes integral , initial value problem , cauchy distribution , analytic semigroup , c0 semigroup , exponential function , operator (biology) , differential operator , pure mathematics , integral equation , first order partial differential equation , biochemistry , chemistry , repressor , transcription factor , gene
Volterra integro-differential equations with kernels of integral operators representable by Stieltjes integrals are investigated. The presented results are based on the approach related to the study of one-parameter semigroups for linear evolution equations. We present the method of reduction of the original initial-value problem for a model integro-differential equation with operator coefficients in a Hilbert space to the Cauchy problem for a first-order differential equation in an extended function space. The existence of the contractive C0-semigroup is proved. An estimate for the exponential decay of the semigroup is obtained.