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 a contractive C0-semigroup is proved. An estimate for the exponential decay of the semigroup is obtained.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 3, In honor of the 70th anniversary of Professor V. M. Filippov, 2021.
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Vlasov, V.V., Rautian, N.A. Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals. J Math Sci 278, 287–305 (2024). https://doi.org/10.1007/s10958-024-06920-9
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DOI: https://doi.org/10.1007/s10958-024-06920-9