Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.278 (2), p.287-305
Main Authors: Vlasov, V. V., Rautian, N. A.
Format: Article
Language:English
Subjects:
Analysis
Cauchy problems
Differential equations
Function space
Hilbert space
Integrals
Linear evolution equations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Semigroups
Volterra integral equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 a contractive C 0 -semigroup is proved. An estimate for the exponential decay of the semigroup is obtained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-06920-9