Geodesic
Approximate symmetries in viscoelasticity
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 115-124 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the framework of approximate symmetries, we investigate a perturbed system of partial differential equations for viscoelastic media with nonlinear dissipation. We completely classify the approximate symmetries and prove a theorem on the relation between the symmetries of two related models. In some physical cases, we find approximate solutions using the generator of the group of transformations taken in the first-order approximation.
Keywords: approximate symmetry, viscoelastic medium
Mots-clés : nonlocal transformation. 
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M. Ruggieri; M. P. Speciale. Approximate symmetries in viscoelasticity. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 115-124. http://geodesic.mathdoc.fr/item/TMF_2016_189_1_a8/

[1] V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov, Matem. sb., 136(178):4(8) (1988), 435–450 | DOI | MR | MR | Zbl

[2] R. K. Gazizov, J. Nonlinear Math. Phys., 3:1–2 (1996), 96–101 | DOI | MR | Zbl

[3] R. K. Gazizov, J. Math. Anal. Appl., 213:1 (1997), 202–228 | DOI | MR | Zbl

[4] N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, v. 1–3, CRC Press, Boca Raton, FL, 1994, 1995 | MR | Zbl

[5] W. I. Fushchych, W. M. Shtelen, N. I. Serov, Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Mathematics and Its Applications, 246, Kluwer, Dordrecht, 1993 | DOI | MR

[6] A. Valenti, “Approximate symmetries for a model describing dissipative media”, Proceedings of 10th International Conference in Modern Group Analysis (MOGRAN X) (Larnaca, Cyprus, October 24–31, 2004), eds. N. H. Ibragimov, C. Sophocleous, P. A. Damianou, Blekinge Institute of Technology, Karlskrona, Sweden, 2005, 236–243

[7] M. Ruggieri, A. Valenti, Bound. Value Probl., 2013 (2013), 143, 8 pp. | DOI | MR | Zbl

[8] M. Ruggieri, M. P. Speciale, Acta Appl. Math., 132:1 (2014), 549–559 | DOI | MR | Zbl

[9] A. Valenti, “Approximate symmetries of aviscoelastic model”, WASCOM 2007, Proceedings of 14th Conference on Waves and Stability in Continuous Media (Baia Samuele, Sicily, Italy, 30 June – 7 July, 2007), eds. N. Manganaro, R. Monaco, S. Rionero, World Sci., Singapore, 2008, 582–588 | DOI | MR | Zbl

[10] M. Ruggieri, A. Valenti, J. Math. Phys., 50:6 (2009), 063506, 9 pp. | DOI | MR | Zbl

[11] M. Ruggieri, A. Valenti, J. Math. Phys., 52:4 (2011), 043520, 7 pp. | DOI | MR | Zbl

[12] M. Ruggieri, Abstr. Appl. Anal., 2012 (2012), 237135, 7 pp. | DOI | MR | Zbl

[13] C. M. Dafermos, J. Differ. Equ., 6:1 (1969), 71–86 | DOI | MR | Zbl

[14] R. C. MacCamy, Indiana Univ. Math. J., 20:3 (1971), 231–238 | DOI | MR | Zbl

[15] M. Ruggieri, M. P. Speciale, Ricerche Mat., 2016, 8 pp., DOI: 10.1007/s11587-016-0282-z | DOI

[16] G. Capriz, “Waves in strings with non-local response”, Mathematical Problems in Continuum Mechanics, Internal Report No. 13 (Trento, 12–17, January, 1981), CRM, Trento, 1981, 12–17

[17] H. M. Cekirge, E. Varley, Philos. Trans. Roy. Soc. London. Ser. A, 273:1234 (1973), 261–313 | DOI | Zbl

[18] C. Rogers, W. F. Shadwick, Bäcklund Transformations and Their Applications, Mathematics in Science and Engineering, 161, Academic Press, New York, 1982 | MR | Zbl