Problem of Longitudinal Vibrations of a Viscoelastic Rod of Maxwell Type-Reference-Cited by-同舟云学术

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Problem of Longitudinal Vibrations of a Viscoelastic Rod of Maxwell Type

Published:2023-05-01 Issue:3 Volume:87 Page:489-498
ISSN:0032-8235
Container-title:Прикладная математика и механика
language:
Short-container-title:Prikladnaâ matematika i mehanika

Author:

Korzyuk V. I.¹²,Rudzko J. V.¹,Kolyachko V. V.²

Affiliation:

1. Institute of Mathematics of the NAS of Belarus

2. Belarusian State University

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.

Publisher

The Russian Academy of Sciences

Reference8 articles.

1. Landau L.D., Lifshitz E.M. Course of Theoretical Physics. in 10 vol. Vol. 7. Theory of Elasticity. Moscow: Fizmatlit, 2003. 264 p. (in Russian)

2. Rzhanitsyn A.R. Theory of Creep. Мoscow: Stroiizdat, 1968. 418 p. (in Russian)

3. Rzhanitsyn A.R. Some Questions of the Mechanics of Systems Deforming in Time. Moscow: GITTL, 1949. 248 p. (in Russian)

4. Strikwerda J.C. Finite Difference Schemes and Partial Differential Equations. 2nd ed. Philadelphia: Soc. for Industr.&Appl. Math., 2004. 439 p.

5. Evans L.C. Partial Differential Equations. 2nd ed. Providence, R.I.: Amer. Math. Soc., 2010. 749 p.

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