Affiliation:
1. Lomonosov Moscow State University
2. Moscow Center of Fundamental and Applied Mathematics
Abstract
We discuss the issues of correct solvability and exponential stability of solutions of abstract integrodifferential equations with kernels of integral operators of general type from the space of functions integrable on the positive semiaxis. The abstract integro-differential equations are studied in this paper are operator models of viscoelasticity theory problems. The proposed approach to the study of these integro-differential equations is related to the application of the semigroups theory and can also be used to study other integro-differential equations containing integral terms of Volterra convolution type.
Publisher
The Russian Academy of Sciences
Reference36 articles.
1. Ильюшин, А.А. Основы математической теории термовязкоупругости / А.А. Ильюшин, Б.Е. Победря. — М. : Наука, 1970. — 280 c.
2. Christensen, R.M. Theory of Viscoelasticity. An Introduction / R.M. Christensen — New York ; London : Academic Press, 1971. — 245 p.
3. Георгиевский, Д.В. Модели теории вязкоупругости / Д.В. Георгиевский. — М. : Ленанд, 2023. — 144 c.
4. Amendola, G. Thermodynamics of Materials with Memory. Theory and Applications / G. Amendola, M. Fabrizio, J.M. Golden. — New York ; Dordrecht ; Heidelberg ; London : Springer, 2012. — 576 p.
5. Gurtin, M.E., General theory of heat conduction with finite wave speed / M.E. Gurtin, A.C. Pipkin // Arch. Rat. Mech. Anal. — 1968. — V. 31. — P. 113–126.