Geodesic
One-dimensional model describing the non-linear viscoelastic response of materials
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 227-246

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In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Classification : 35A09, 35M33, 45G10, 45K05, 74D10, 74H20, 74H40
Keywords: viscoelasticity; integrodifferential equation; classical solution; global existence; implicit constitutive relations 
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     author = {B\'arta, Tom\'a\v{s}},
     title = {One-dimensional model describing the non-linear viscoelastic response of materials},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     zbl = {06391540},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a8/}
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Bárta, Tomáš. One-dimensional model describing the non-linear viscoelastic response of materials. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 227-246. http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a8/