Periodic longitudinal motions of a viscoelastic rod

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http://www.yokohamapublishers.jp/online2/oppafa/vol4/p671.html

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http://hdl.handle.net/11603/36912

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UMBC Faculty Collection
UMBC Mathematics and Statistics Department

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0001-8594-0568

Date

2019

Type of Work

journal articles
Text

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Program

Citation of Original Publication

Biswas, Animikh, and Thomas I. Seidman. “Periodic Longitudinal Motions of a Viscoelastic Rod” Pure and Apllied Functional Analysis 4, no. 4 (2019): 671–83. http://www.yokohamapublishers.jp/online2/oppafa/vol4/p671.html

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Abstract

In this paper, we investigate the existence of a time-periodic solution for a quasilinear hyperbolic-parabolic equation arising in the study of longitudinal motion of a one-dimensional, viscoelastic rod. By employing the implicit function theorem, we show that when the specified forcing is sufficiently small, a nontrivial time-periodic solution exists.