Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals
- Authors: Vlasov V.V.1,2, Rautian N.A.1,2
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Affiliations:
- Lomonosov Moscow State University
- Moscow Center of Fundamental and Applied Mathematics
- Issue: Vol 67, No 3 (2021): Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov
- Pages: 507-525
- Section: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327728
- DOI: https://doi.org/10.22363/2413-3639-2021-67-3-507-525
- ID: 327728
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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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