Abstract
Existence and uniqueness of the solution of the Cauchy problem is proved for a system of integrodifferential equations of the hereditary theory of viscoelasticity. A method of constructing an approximate solution is proposed. An estimate of the error of the approximate solution is presented.
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Literature cited
M. A. Koltunov and I. E. Troyanovskii, “Formulation of a problem of the geometrically nonlinear theory of elasticity”, Mekh. Polim., No. 2, 234–240 (1975).
A. N. Filatov, Averaging Methods in Differential and Integrodifferential Equations [in Russian], Tashkent (1971).
Yu. N. Rabotnov, Creep of Structural Elements [in Russian], Moscow (1967).
J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press (1967).
Additional information
Moscow Institute of Electronic Machine Construction. Translated from Mekhanika Polimerov, No. 6, pp. 969–975, November–December, 1975.
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Koltunov, M.A., Morgunov, B.I. & Troyanovskii, I.E. Solution of the Cauchy problem for a system of integrodifferential equations of viscoelasticity. Polymer Mechanics 11, 828–833 (1975). https://doi.org/10.1007/BF00857601
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DOI: https://doi.org/10.1007/BF00857601