Relativistic and nonrelativistic elastodynamics with small shear strains
Tahvildar-Zadeh, A. Shadi
Annales de l'I.H.P. Physique théorique, Tome 69 (1998), p. 275-307 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1998-01-01
@article{AIHPA_1998__69_3_275_0,
     author = {Tahvildar-Zadeh, A. Shadi},
     title = {Relativistic and nonrelativistic elastodynamics with small shear strains},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {69},
     year = {1998},
     pages = {275-307},
     mrnumber = {1648985},
     zbl = {0930.74008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1998__69_3_275_0}
}

Tahvildar-Zadeh, A. Shadi. Relativistic and nonrelativistic elastodynamics with small shear strains. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) pp. 275-307. http://gdmltest.u-ga.fr/item/AIHPA_1998__69_3_275_0/

[1] E. Bernardi and T. Nishitani, Remarks on symmetrization of 2 x 2 systems and the characteristic manifolds. Osaka J. Math., Vol. 29, 1992, pp. 129-134. | MR 1153184 | Zbl 0764.35058

[2] B. Carter and H. Quintana, Foundations of general relativistic high-pressure elasticity theory. Proc. R. Soc. Lond., A. 331, 1972, pp. 57-83. | MR 311270 | Zbl 0249.73093

[3] D. Christodoulou, Lecture notes of course taught at Princeton University, Fall 1995.

[4] D. Christodoulou, Self-gravitating relativistic fluids: A two-phase model. Arch. Rational Mech. Anal., Vol. 130, 1995, pp. 343-400. | MR 1346362 | Zbl 0841.76097

[5] D. Christodoulou, On the geometry and dynamics of crystalline continua. Ann. Inst. H. Poincaré Phys. Théor, to appear. | Numdam | MR 1648987 | Zbl 0916.73013

[6] G.F.D. Duff, The Cauchy problem for elastic waves in an anisotropic medium. Phil. Trans. Roy. Soc. A., Vol. 252, 1960, pp. 249-273. | MR 111293 | Zbl 0103.42502

[7] L. Hörmander, Hyperbolic systems with double characteristics. Comm. Pure. Appl. Math., Vol. 46, 1993, pp. 261-301. | MR 1199200 | Zbl 0803.35082

[8] F. John, Algebraic conditions for hyperbolicity of systems of partial differential equations. Comm. Pure. Appl. Math., Vol. 31, 1978, pp. 89-106. | Zbl 0381.35059

[9] F. John, Formation of singularities in elastic waves. Lec. Notes in Phys., Vol. 195, 1984, pp. 190-214. | Zbl 0563.73022

[10] J. Kijowski and G. Magli, Relativistic elastomechanics as a Lagrangian field theory. Journal of Geometry and Physics, Vol. 9, 1992, pp. 207-223. | Zbl 0771.73004

[11] S. Klainerman, Long-time behavior of solutions to nonlinear evolution equations. Arch. Rational Mech. Anal, Vol. 78(1), 1982, pp. 73-98. | Zbl 0502.35015

[12] G.A. Maugin, Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids. Ann. Inst. H. Poincaré Phys. Théor., Vol. 28, 1978, p. 155-185. | Numdam | Zbl 0375.73025

[13] T.C. Sideris, Formation of singularities in three-dimensional compressible fluids. Comm. Math. Phys., Vol. 101, 1985, pp. 475-485. | Zbl 0606.76088

[14] T.C. Sideris, The null condition and global existence of nonlinear elastic waves. Invent. Math., Vol. 123, 1996, pp. 323-342. | Zbl 0844.73016

[15] J.M. Souriau, Géométrie et Relativité. Hermann, Paris, 1964. | Zbl 0117.22204