Abstract
Abstract Volterra integro-differential equations that are operator models of viscoelasticity problems are investigated. The class of equations under consideration also includes the Gurtin–Pipkin integro-differential equations describing heat propagation in media with memory. As kernels of integral operators, it is possible to use, in particular, sums of decreasing exponents or sums of Rabotnov functions with positive coefficients, which are widely applied in the theory of viscoelasticity and heat propagation theory.
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Funding
Theorems 1–3 were proved under the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics. Theorem 4 was proved under the support of the Ministry of Education and Science of the Russian Federation as part of the state assignment, project no. FSSF-2023-0016.
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Translated by I. Ruzanova
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Rautian, N.A. Study of Volterra Integro-Differential Equations by Methods of Semigroup Theory. Dokl. Math. 108, 402–405 (2023). https://doi.org/10.1134/S1064562423701272
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DOI: https://doi.org/10.1134/S1064562423701272