On the null condition for nonlinearly elastic solids

Archives of Mechanics

Volumn 58, Issue 4-5, 2006, Pages 339-361

  Domanski W ^a   Ogden, R W ^b  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750459082     PISSN: 03732029     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. T.J.R. Hughes, T. Kato, J.E. Marsden, Well-posed quasi linear second order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rational Mech. Anal., 63, 274-294, 1976.
2. R.J. Diperna, Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Diff. Eqs., 20, 187-212, 1976.
3. S. Demoulini, D.M.A. Stuart, A.E. Tzavaras, A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy, Arch. Rational Mech. Anal., 157, 325-344, 2001.
4. S. Klainerman, The null condition and global existence to nonlinear wave equations, Lectures in Applied Mathematics, 23, 293-326, 1986.
5. T.C. Sideris, The null condition and global existence of nonlinear elastic waves, Inven. Math., 123, 323-342, 1996.
6. T.C. Sideris, Nonresonance and global existence of prestressed nonlinear elastic waves, Ann. of Math., 151, 849-874, 2000.
7. R. Agemi, Global existence of nonlinear elastic waves, Inven. Math., 142, 225-250, 2000.
8. A. Shadi Tahvildar-Zadeh, Relativistic and non-relativistic elastodynamics with small shear strains, Ann. Inst. H. Poincare Phys. Theor., 69, 275-307, 1998.
9. F. John, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math., 26, 377-405, 1974.
10. R.W. Ogden, Nonlinear elastic deformations, Dover 1997.
11. R.W. Ogden, Nonlinear elasticity with application to material modelling, Lecture Notes 6, Center of Excellence for Advanced Materials and Structures, AMAS, IFTR PAS, Warsaw 2003.
12. J. Xin, Some remarks on the null condition for nonlinear elastodynamic system, Chin. Ann. Math. Ser. B, 23, 311-316, 2002.
13. W. Domański and R. Young, Interaction of plane waves in nonlinear elasticity, submitted.
14. F. D. Murnaghan, Finite deformation of an elastic solid, Dover 1967.
15. W. Domański, Weakly nonlinear elastic plane waves in a cubic crystal, Contemp. Math., 255, 45-61, 2000.
16. P.G. Ciarlet, Mathematical elasticity, Vol. 1: Three-dimensional elasticity, North Holland, Amsterdam 1988.
17. X. Jiang and R.W. Ogden, On azimuthal shear of a circular cylindrical tube of compressible elastic material, Quart. J. Mech. Appl. Math., 51, 143-158, 1998.