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References
Ball, J. M., Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil. Trans. R. Soc. London A 306 (1982), 557–611.
Cáceres, C. H., & D. S. Wilkinson, Large strain behavior of a superplastic copper alloy II. Cavitation and Fracture. Acta Metall. 32 (1984), 423–434.
Dafermos, C. M., The entropy rate admissibility criterion for solutions of hyperbolic conservation laws. J. Diff. Eqns. 14 (1973), 202–212.
Dafermos, C. M., The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70 (1979), 167–179.
Dafermos, C. M., Hyperbolic systems of conservation laws. Systems of Nonlinear Partial Differential Equations (J. M. Ball, ed.). Dordrecht: D. Reidel (1983), 25–70.
Elliot, D., Crack tip processes leading to fracture, The Practical Implications of Fracture Mechanisms. London: Institution of Metallurgists (1973), 21–27.
Hahn, G. T., & A. R. Rosenfield, Metallurgical factors affecting fracture toughness in aluminum alloys. Met. Trans. 6 A (1975), 653–668.
Hancock, J. W., & A. C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J. Mech. Phys. Solids 24 (1976), 147–169.
Horgan, C. O., & R. Abeyaratne, A bifurcation problem for a compressible non-linearly elastic medium: growth of a micro-void. J. Elasticity 16 (1986), 189–200.
James, R. D., The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73 (1980), 125–158.
Lax, P. D., Hyperbolic systems of conservation laws. Comm. Pure Appl. Math. 10 (1957), 537–566.
Lax, P. D., Shock waves and entropy. Contributions to Functional Analysis (E. A. Zarantonelo, ed.). New York: Academic Press (1976), 603–634.
Podio-Guidugli, P., G. Vergara Caffarelli, & E. G. Virga, Discontinuous energy minimizers in nonlinear elastostatics: an example of J. Ball revisited. J. Elasticity 16 (1986), 75–96.
Shearer, M., Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type. Arch. Rational Mech. Anal. 93 (1986), 45–59.
Sivaloganathan, J., Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity. Arch. Rational Mech. Anal. 96 (1986), 97–136.
Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal. 81 (1983), 301–315.
Stuart, C. A., Radially symmetric cavitation for hyperelastic materials. Ann. Inst. Henri Poincaré: Nonlinear Anal. 2 (1985), 33–66.
Truesdell, C., & R. Toupin, The classical field theories. Handbuch der Physik. III/1 (S. Flügge, ed.). Berlin: Springer-Verlag, 1960.
Wheeler, L., A uniqueness theorem for the displacement problem in finite elastodynamics. Arch. Rational Mech. Anal. 63 (1970), 183–189.
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Pericak-Spector, K.A., Spector, S.J. Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics. Arch. Rational Mech. Anal. 101, 293–317 (1988). https://doi.org/10.1007/BF00251490
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DOI: https://doi.org/10.1007/BF00251490