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

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Abstract

Abstract 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.

About the authors

V. V. Vlasov

Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics

Author for correspondence.
Email: victor.vlasov@math.msu.ru
Moscow, Russia

N. A. Rautian

Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics

Email: nadezhda.rautian@math.msu.ru
Moscow, Russia

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