Abstract
We study the well-posed solvability of initial value problems for Volterra integro-differential equations in a Hilbert space with kernels of integral operators represented by Stieltjes integrals. The approach used in the paper is related to the application of the theory of operator semigroups.
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Funding
This work was supported in part by the Ministry of Science and Higher Education of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-284 and with the partial financial support of the Interdisciplinary Scientific and Educational School of Moscow University “Mathematical Methods of Analysis of Complex Systems.”
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Translated by V. Potapchouck
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Vlasov, V.V., Rautian, N.A. Well-Posed Solvability of Volterra Integro-Differential Equations in Hilbert Spaces. Diff Equat 58, 1410–1426 (2022). https://doi.org/10.1134/S0012266122010010X
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DOI: https://doi.org/10.1134/S0012266122010010X