On a transmission problem in elasticity

Christodoulos Athanasiadis; Ioannis G. Stratis

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 3, page 281-300
  • ISSN: 0066-2216

Abstract

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The transmission problem for the reduced Navier equation of classical elasticity, for an infinitely stratified scatterer, is studied. The existence and uniqueness of solutions is proved. Moreover, an integral representation of the solution is constructed, for both the near and the far field.

How to cite

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Christodoulos Athanasiadis, and Ioannis G. Stratis. "On a transmission problem in elasticity." Annales Polonici Mathematici 68.3 (1998): 281-300. <http://eudml.org/doc/270557>.

@article{ChristodoulosAthanasiadis1998,
abstract = {The transmission problem for the reduced Navier equation of classical elasticity, for an infinitely stratified scatterer, is studied. The existence and uniqueness of solutions is proved. Moreover, an integral representation of the solution is constructed, for both the near and the far field.},
author = {Christodoulos Athanasiadis, Ioannis G. Stratis},
journal = {Annales Polonici Mathematici},
keywords = {transmission problem; infinitely stratified scatterer; scattering amplitudes; integral representation of solution; reduced Navier equation; existence; uniqueness},
language = {eng},
number = {3},
pages = {281-300},
title = {On a transmission problem in elasticity},
url = {http://eudml.org/doc/270557},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Christodoulos Athanasiadis
AU - Ioannis G. Stratis
TI - On a transmission problem in elasticity
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 3
SP - 281
EP - 300
AB - The transmission problem for the reduced Navier equation of classical elasticity, for an infinitely stratified scatterer, is studied. The existence and uniqueness of solutions is proved. Moreover, an integral representation of the solution is constructed, for both the near and the far field.
LA - eng
KW - transmission problem; infinitely stratified scatterer; scattering amplitudes; integral representation of solution; reduced Navier equation; existence; uniqueness
UR - http://eudml.org/doc/270557
ER -

References

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  1. [1] C. Athanasiadis and I. G. Stratis, Low-frequency acoustic scattering by an infinitely stratified scatterer, Rend. Mat. Appl. 15 (1995), 133-152. 
  2. [2] C. Athanasiadis and I. G. Stratis, Parabolic and hyperbolic diffraction problems, Math. Japon. 43 (1996), 37-45. 
  3. [3] C. Athanasiadis and I. G. Stratis, On some elliptic transmission problems, Ann. Polon. Math. 63 (1996), 137-154. 
  4. [4] P. J. Barrat and W. D. Collins, The scattering cross-section of an obstacle in an elastic solid for plane harmonic waves, Proc. Cambridge Philos. Soc. 61 (1965), 969-981. 
  5. [5] G. Caviglia and A. Morro, Inhomogeneous Waves in Solids and Fluids, World Sci., London, 1992. 
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  8. [8] G. Fichera, Existence theorems in elasticity, in: Handbuch der Physik, Via/2, Springer, Berlin, 1972, 347-389. 
  9. [9] D. S. Jones, Low-frequency scattering in elasticity, Quart. J. Mech. Appl. Math. 34 (1981), 431-451. Zbl0473.73026
  10. [10] D. S. Jones, A uniqueness theorem in elastodynamics, Appl. Math. 37 (1984), 121-142. Zbl0562.73010
  11. [11] K. Kiriaki and D. Polyzos, The low-frequency scattering theory for a penetrable scatterer with an impenetrable core in an elastic medium, Internat. J. Engrg. Sci. 26 (1988), 1143-1160. Zbl0676.73014
  12. [12] V. D. Kupradze, Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem, 1965. 
  13. [13] V. D. Kupradze (ed.), Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam, 1979. 
  14. [14] D. Polyzos, Low-frequency elastic scattering theory for a multi-layered scatterer with dyadic incidence, submitted. 
  15. [15] P. C. Sabatier, On the scattering by discontinuous media, in: Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, W. Rundell (eds.), SIAM, Philadelphia, 1990, 85-100. 
  16. [16] L. T. Wheeler and E. Sternberg, Some theorems in classical elastodynamics, Arch. Rational Mech. Anal. 31 (1968), 51-90. Zbl0187.47003

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