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September  2013, 2(3): 471-493. doi: 10.3934/eect.2013.2.471

Traction, deformation and velocity of deformation in a viscoelastic string

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

Received  September 2012 Revised  March 2013 Published  July 2013

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.
Citation: Luciano Pandolfi. Traction, deformation and velocity of deformation in a viscoelastic string. Evolution Equations & Control Theory, 2013, 2 (3) : 471-493. doi: 10.3934/eect.2013.2.471
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