Geodesic
The wave field of a point source that acts on the impermeable stress free boundary of a Biot half-plane
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 54-64 
G. L. Zavorokhin. The wave field of a point source that acts on the impermeable stress free boundary of a Biot half-plane. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 54-64. http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a4/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Initial boundary value problem of wave propagation in half-plane filled with fluid-saturated porous solid is considered. Biot's medium is isotropic homogeneous and pores are closed on the boundary. Using complex analysis techniques, explicit formulae for displacements in elastic and fluid phases are obtained.

[1] M. A. Biot, “Theory of propagation of elastic waves in fluid-saturated porous solid”, J. Acoust. Soc. Amer., 28:2 (1956), 168–191 | DOI | MR

[2] L. A. Molotkov, “Ob istochnikakh, deistvuyuschikh na svobodnoi granitse poristoi sredy Bio, i ob otrazhenii voln na etoi granitse”, Zap. nauchn. semin. POMI, 264, 2000, 217–237 | MR | Zbl

[3] G. L. Zavorokhin, “Volnovoe pole ot tochechnogo istochnika, deistvuyuschego na otkrytoi granitse poluploskosti Bio”, Zap. nauchn. semin. POMI, 393, 2011, 101–110 | MR

[4] L. A. Molotkov, “Rasprostranenie voln v izolirovannom poristom sloe Bio s zakrytymi porami na granitsakh”, Zap. nauchn. semin. POMI, 354, 2008, 173–189 | Zbl

[5] L. A. Molotkov, “Normalnye volny v poristom sloe s otkrytymi porami na odnoi granitse i s zakrytymi porami na drugoi granitse”, Zap. nauchn. semin. POMI, 393, 2011, 178–190 | MR

[6] N. S. Gorodetskaya, “Volny na granitse poristo-uprugogo poluprostranstva. I. Svobodnaya granitsa”, Akustichnii visnik, 8:1–2 (2005), 28–41

[7] L. A. Molotkov, “Rasprostranie normalnykh voln v poristom sterzhne s zakrytymi porami na granitsakh”, Zap. nauchn. semin. POMI, 393, 2011, 191–210 | MR

[8] L. A. Molotkov, “Rasprostranie normalnykh voln v poristom sterzhne s otkrytymi porami na granitsakh”, Zap. nauchn. semin. POMI, 393, 2011, 211–223 | MR

[9] G. I. Petrashen, G. I. Marchuk, K. I. Ogurtsov, “O zadache Lemba v sluchae poluprostranstva”, Uch. Zap. LGU, 35:21 (1950), 71–118

[10] V. M. Babich, S. K. Kochuguev, O metode V. I. Smirnova – S. L. Soboleva yavnogo resheniya zadach matematicheskoi teorii difraktsii, Preprint 1/2002, POMI

[11] V. I. Smirnoff, S. L. Soboleff, Sur une methode nouvelle dans le probleme plan des vibrations elastiques, Tr. Seism. inst., 20, AN SSSR, L., 1932