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Online ISSN 1552-4485; Print ISSN 0033-569X
Travelling waves in hyperelastic rods
Authors:
Stuart S. Antman and Tai Ping Liu
Journal:
Quart. Appl. Math. 36 (1979), 377-399
MSC:
Primary 73D99; Secondary 35Q99
DOI:
https://doi.org/10.1090/qam/520121
MathSciNet review:
520121
Full-text PDF Free Access
References | Similar Articles | Additional Information
- S. S. Antman, Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods [ MR1375818 (96m:73020)], Mechanics: from theory to computation, Springer, New York, 2000, pp. 1–18. MR 1766356
- Stuart S. Antman, Kirchhoff’s problem for nonlinearly elastic rods, Quart. Appl. Math. 32 (1974/75), 221–240. MR 667026, DOI https://doi.org/10.1090/S0033-569X-1974-0667026-4
- Stuart S. Antman and Kathleen B. Jordan, Qualitative aspects of the spatial deformation of non-linearly elastic rods, Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 85–105. MR 408386, DOI https://doi.org/10.1017/S0308210500016309
- James F. Bell, The experimental foundations of solid mechanics, Mechanics of Solids, I, Springer-Verlag, Berlin, 1984. Reprint of the 1973 original. MR 763158
- Constantine M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Differential Equations 14 (1973), 202–212. MR 328368, DOI https://doi.org/10.1016/0022-0396%2873%2990043-0
- G. Kirchhoff, Ueber das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes, J. Reine Angew. Math. 56 (1859), 285–313 (German). MR 1579104, DOI https://doi.org/10.1515/crll.1859.56.285
- P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI https://doi.org/10.1002/cpa.3160100406
- Tai Ping Liu, The Riemann problem for general systems of conservation laws, J. Differential Equations 18 (1975), 218–234. MR 369939, DOI https://doi.org/10.1016/0022-0396%2875%2990091-1 A. E. H. Love, A treatise on the mathematical theory of elasticity, 4th ed., Cambridge University Press, 1927
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Article copyright:
© Copyright 1979
American Mathematical Society