Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium

Alessia Berti

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 521-533
  • ISSN: 0392-4033

Abstract

top
The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed.

How to cite

top

Berti, Alessia. "Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 521-533. <http://eudml.org/doc/290438>.

@article{Berti2007,
abstract = {The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed.},
author = {Berti, Alessia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {521-533},
publisher = {Unione Matematica Italiana},
title = {Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium},
url = {http://eudml.org/doc/290438},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Berti, Alessia
TI - Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 521
EP - 533
AB - The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed.
LA - eng
UR - http://eudml.org/doc/290438
ER -

References

top
  1. BURRIDGE, R., The Gelfand-Levitan, the Marchenko and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of implulse-response problems, Wave Motion, 2 (4) (1980), 305-323. Zbl0444.45010MR593133DOI10.1016/0165-2125(80)90011-6
  2. CAVIGLIA, C. - MORRO, M., Existence and uniqueness in the reflection-transmission problem, Quart. J. Mech. Appl. Math., 52 (4) (1999), 543-564. Zbl0962.74028MR1730008DOI10.1093/qjmam/52.4.543
  3. CAVIGLIA, C. - MORRO, M., Existence and uniqueness of the solution in the frequency domain for the reflection-transmission problem in a viscoelastic layer, Arch. Mech., 56 (1) (2004), 59-82. Zbl1080.74030MR2044109
  4. CODDINGTON, E. A. - LEVINSON, N., Theory of ordinary differential equations, International series in Pure and Applied Mathematics, 1955. MR69338
  5. DEIFT, P. - TRUBOWITZ, E., Inverse scattering on the line, Comm. Pure Appl. Math., 32 (2) (1979), 121-251. Zbl0388.34005MR512420DOI10.1002/cpa.3160320202
  6. DESTRADE, M. - MARTIN, P. A. - TING, T. C. T., The incompressible limit in linear anisotropic elasticity with applications to surface waves and elastostatic, J. Mech. Phys. Solids, 50 (7) (2002) 1453-1468. Zbl1038.74008MR1903721DOI10.1016/S0022-5096(01)00121-1
  7. ERINGEN, A. C., Continuum Physics. Vol II Continuum Mechanics of single-substance bodies, Academic Press, New York - London, 1975. MR468443
  8. FABRIZIO, M. - MORRO, A., Mathematical problems in linear viscoelasticity, Am. Math. Soc. Transl., 65 (2) (1967), 139-166. MR1153021DOI10.1137/1.9781611970807
  9. FADDEEV, L. D., Properties of the S-matrix of the one-dimensional Schrödinger equation, Am. Math. Soc. Transl., 65 (2) (1967), 139-166. 
  10. FU, Y. - MIELKE, A., A new identify for the surface-impedance matrix and its application to the determination of surface-wave speeds, Comm. Pure Appl. Math., 32 (2) (1979), 121-251. 
  11. GRINBERG, N. I., Inverse scattering problem for an elastic layered medium, Inverse Problems, 7 (4) (1991), 567-576. Zbl0738.73020MR1122037
  12. LANCASTER, P. - TISMENETSKY, M., The theory of matrices, Academic, Orlando1985. Zbl0558.15001MR792300
  13. STROH, A. N., Steady state problems in anisotropic elasticity, J. Math. and Phys., 41 (1962), 77-103. Zbl0112.16804MR139306
  14. SYLVESTER, J. - WINEBRENNER, D. - GYLYS-COLWELL, F., Layer stripping for the Helmholtz equation, SIAM J. Appl. Math., 56 (3) (1996), 736-754. Zbl0851.34011MR1389751DOI10.1137/S0036139995280257
  15. SYLVESTER, J. - WINEBRENNER, D., Linear and nonlinear inverse scattering, SIAM J. Appl. Math., 59 (2) (1999), 669-699. Zbl0930.34066MR1654391DOI10.1137/S0036139997319773

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.