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.
@article{bwmeta1.element.bwnjournal-article-apmv68z3p281bwm,
author = {Christodoulos Athanasiadis and Ioannis G. Stratis},
title = {On a transmission problem in elasticity},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {281-300},
zbl = {0904.73011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z3p281bwm}
}
Christodoulos Athanasiadis; Ioannis G. Stratis. On a transmission problem in elasticity. Annales Polonici Mathematici, Tome 69 (1998) pp. 281-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z3p281bwm/
[000] [1] C. Athanasiadis and I. G. Stratis, Low-frequency acoustic scattering by an infinitely stratified scatterer, Rend. Mat. Appl. 15 (1995), 133-152.
[001] [2] C. Athanasiadis and I. G. Stratis, Parabolic and hyperbolic diffraction problems, Math. Japon. 43 (1996), 37-45.
[002] [3] C. Athanasiadis and I. G. Stratis, On some elliptic transmission problems, Ann. Polon. Math. 63 (1996), 137-154.
[003] [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.
[004] [5] G. Caviglia and A. Morro, Inhomogeneous Waves in Solids and Fluids, World Sci., London, 1992.
[005] [6] G. Dassios and K. Kiriaki, The low-frequency theory of elastic wave scattering, Quart. Appl. Math. 42 (1984), 225-248. | Zbl 0553.73016
[006] [7] R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Physical Origins and Classical Methods, Springer, Berlin, 1990. | Zbl 0683.35001
[007] [8] G. Fichera, Existence theorems in elasticity, in: Handbuch der Physik, Via/2, Springer, Berlin, 1972, 347-389.
[008] [9] D. S. Jones, Low-frequency scattering in elasticity, Quart. J. Mech. Appl. Math. 34 (1981), 431-451. | Zbl 0473.73026
[009] [10] D. S. Jones, A uniqueness theorem in elastodynamics, Appl. Math. 37 (1984), 121-142. | Zbl 0562.73010
[010] [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. | Zbl 0676.73014
[011] [12] V. D. Kupradze, Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem, 1965.
[012] [13] V. D. Kupradze (ed.), Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam, 1979.
[013] [14] D. Polyzos, Low-frequency elastic scattering theory for a multi-layered scatterer with dyadic incidence, submitted.
[014] [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.
[015] [16] L. T. Wheeler and E. Sternberg, Some theorems in classical elastodynamics, Arch. Rational Mech. Anal. 31 (1968), 51-90. | Zbl 0187.47003