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Problem of Longitudinal Vibrations of a Viscoelastic Rod of Maxwell Type
- Authors: Korzyuk V.I.1,2, Rudzko J.V.1, Kolyachko V.V.2
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Affiliations:
- Institute of Mathematics of the NAS of Belarus
- Belarusian State University
- Issue: Vol 87, No 3 (2023)
- Pages: 489-498
- Section: Articles
- URL: https://freezetech.ru/0032-8235/article/view/675131
- DOI: https://doi.org/10.31857/S0032823523030086
- EDN: https://elibrary.ru/ZTPLMI
- ID: 675131
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Abstract
In this paper, we study well-posedness in the sense of Hadamard of the Cauchy problem for a one-dimensional hyperbolic system of partial differential equations describing the longitudinal vibrations of a viscoelastic rod of Maxwell type with constant cross-section. We discuss some properties of the system and its solutions: the conservation of modified “energy”, the finite propagation speed, dispersion, and dissipation of solutions.
About the authors
V. I. Korzyuk
Institute of Mathematics of the NAS of Belarus; Belarusian State University
Author for correspondence.
Email: korzyuk@bsu.by
Belarus, Minsk; Belarus, Minsk
J. V. Rudzko
Institute of Mathematics of the NAS of Belarus
Author for correspondence.
Email: janycz@yahoo.com
Belarus, Minsk
V. V. Kolyachko
Belarusian State University
Author for correspondence.
Email: vlad.kolyachko@yandex.ru
Belarus, Minsk
References
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- Evans L.C. Partial Differential Equations. 2nd ed. Providence, R.I.: Amer. Math. Soc., 2010. 749 p.
- Korzyuk V.I., Rudzko J.V. Classical solution of the initial-value problem for a one-dimensional quasilinear wave equation // Dokl. Nat. Acad. of Sci. Belarus, 2023, vol. 67, no. 1, pp. 14–19.
- Polyanin A.D. Handbook of Linear Partial Differential Equations for Engineers and Scientists. Boca Raton: Chapman & Hall/CRC, 2002. 800 p.
- Korzyuk V.I., Rudzko J.V. А particular solution of a problem for a system of equations from mechanics with nonsmooth Cauchy conditions // Proc. of the Nat. Acad. of Sci. Belarus. Ser. Phys.&Math., 2022, vol. 58, no. 3, pp. 300–311. (in Russian)
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