Abstract
The paper studies the properties of a linear operator that is the generator of a semigroup associated with Volterra integro-differential equations in Hilbert spaces. These integro-differential equations can be realized as partial integro-differential equations arising in the theory of viscoelasticity and the theory of heat propagation in media with memory and have a number of other important applications. The results obtained in the paper can be used to study the behavior of and obtain estimates for the solutions of Volterra integro-differential equations.
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Funding
The proof of Theorem 7 and Lemma 1 was supported by the Russian Foundation for Basic Research, project no. 20-01-00288 A. The proof of Theorem 8 was supported by the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University “Mathematical Methods for the Analysis of Complex Systems.”
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Rautian, N.A. On the Properties of the Generators of Semigroups Associated with Volterra Integro-Differential Equations. Diff Equat 57, 1652–1664 (2021). https://doi.org/10.1134/S0012266121120119
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DOI: https://doi.org/10.1134/S0012266121120119