Singularity problems in linear elastodynamics

Bruno Carbonaro; Remigio Russo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)

  • Volume: 18, Issue: 1, page 103-133
  • ISSN: 0391-173X

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Carbonaro, Bruno, and Russo, Remigio. "Singularity problems in linear elastodynamics." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.1 (1991): 103-133. <http://eudml.org/doc/84091>.

@article{Carbonaro1991,
author = {Carbonaro, Bruno, Russo, Remigio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {acoustic tensor; unbounded three-dimensional body; hyperbolicity condition; internal and external energy inequality; uniqueness; work and energy theorems; local domain of influence theorem; thermodynamical domain of influence},
language = {eng},
number = {1},
pages = {103-133},
publisher = {Scuola normale superiore},
title = {Singularity problems in linear elastodynamics},
url = {http://eudml.org/doc/84091},
volume = {18},
year = {1991},
}

TY - JOUR
AU - Carbonaro, Bruno
AU - Russo, Remigio
TI - Singularity problems in linear elastodynamics
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 1
SP - 103
EP - 133
LA - eng
KW - acoustic tensor; unbounded three-dimensional body; hyperbolicity condition; internal and external energy inequality; uniqueness; work and energy theorems; local domain of influence theorem; thermodynamical domain of influence
UR - http://eudml.org/doc/84091
ER -

References

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  1. [1] M.E. Gurtin, The linear theory of elasticity, in Handbuch der Physik (ed. C. Truesdell), vol. VIa/2, Springer (1971). 
  2. [2] L.T. Wheeler - E. Sternberg, Some theorems in classical elastodynamics, Arch. Rational Mech. Anal.31 (1968), 51-90. Zbl0187.47003MR1553519
  3. [3] L.T. Wheeler, Some results in the linear dynamical theory of anisotropic elastic solids, Quart. Appl. Math.28 (1970), 91-101. Zbl0219.73007MR269162
  4. [4] L.T. Wheeler, On the uniqueness of solutions for the displacement problem in linear elastodynamics, J. Elasticity1 (1971), 121-124. MR475142
  5. [5] B. Carbonaro - R. Russo, Energy inequalities and the domain of influence theorem in classical elastodynamics, J. Elasticity14 (1984), 163-174. Zbl0547.73011MR747058
  6. [6] B. Carbonaro - R. Russo, The work and energy theorem and Graffi's reciprocity relation for hyperelastic bodies that may stiffen at infinity, in Atti del 7° Congresso Nazionale AIMETA (Trieste, 2-5 ottobre 1984), vol. 2, Trieste (1984), 37-46. 
  7. [7] B. Carbonaro - R. Russo, The uniqueness problem in the dynamical theory of linear hyperelasticity in unbounded regions, in Atti del 7° Congresso Nazionale AIMETA (Trieste, 2-5 ottobre 1984), vol. 2, Trieste (1984), 47-56. 
  8. [8] B. Carbonaro - R. Russo, On the dynamical behaviour of an elastic body around a point where the acoustic tensor tends either to zero or to infinity, in III Meeting: Waves and Stability in Continuous Media (Atti). Laterza, Bari1988. 
  9. [9] (a) B. Carbonaro, Some examples of nonuniqueness of solutions to the equation of linear elastodynamics, J. Elasticity17 (1987), 207-222; (b) B. Carbonaro, Addendum to "Some example of nonuniqueness of solutions to the equation of linear elastodynamics", J. Elasticity19 (1988), 93-98. Zbl0622.73003MR888316
  10. [10] J.K. Knowles, On the dissipation associated with equilibrium shocks in finite elasticity, J. Elasticity9 (1979). Zbl0407.73037MR535274
  11. [11] R. Russo, On the dynamics of an elastic body containing a moving crack, J. Elasticity16 (1986), 367-374. Zbl0606.73111MR868768
  12. [12] B. Carbonaro - R. Russo, Sharp uniqueness classes in linear elastodynamics, to appear. Zbl0760.73011MR1149471
  13. [13] M. Fabrizio - A. Hanyga, Mixed problems for linear hyperbolic equation with unbounded coefficients, Ann. Univ. Ferrara, Sez. VII, 32 (1986). 
  14. [14] A.E. Hurd - D.H. Sattinger, Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. Amer. Math. Soc.132 (1968), 159-174. Zbl0155.16401MR222457

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