Traction, deformation and velocity of deformation in a viscoelastic string

Luciano Pandolfi

doi:10.3934/eect.2013.2.471

Article Contents

2013, Volume 2, Issue 3: 471-493. Doi: 10.3934/eect.2013.2.471

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Traction, deformation and velocity of deformation in a viscoelastic string

Luciano Pandolfi^1,

1.
Politecnico di Torino, di Scienze Matematiche "Giuseppe Luigi Lagrange", Corso Duca degli Abruzzi 24, 10129 Torino

Received: August 31, 2012

Revised: February 28, 2013

Published: August 2013

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Abstract

In this paper we consider a viscoelastic string whose deformation is controlled at one end. We study the relations and the controllability of the couples traction/velocity and traction/deformation and we show that the first couple behaves very like as in the purely elastic case, while new phenomena appears when studying the couple of the traction and the deformation. Namely, while traction and velocity are independent (for large time), traction and deformation are related at each time but the relation is not so strict. In fact we prove that an arbitrary number of ``Fourier'' components of the traction and, independently, of the deformation can be assigned at any time.

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Mathematics Subject Classification: Primary: 35Q93, 74D05, 76A10; Secondary: 45K05, 93B03.

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