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...

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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
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description 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.
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subjects Analysis
Cauchy problems
Differential equations
Function space
Hilbert space
Integrals
Linear evolution equations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Semigroups
Volterra integral equations
title Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals
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