@article{TSP_2011_28_28_a3,
author = {A. A. Gavrikov and A. S. Shamaev},
title = {Some problems in acoustics of emulsions},
journal = {Trudy Seminara im. I.G. Petrovskogo},
pages = {114--146},
year = {2011},
volume = {28},
number = {28},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TSP_2011_28_28_a3/}
}
A. A. Gavrikov; A. S. Shamaev. Some problems in acoustics of emulsions. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 28 (2011) no. 28, pp. 114-146. http://geodesic.mathdoc.fr/item/TSP_2011_28_28_a3/
[1] Bakhvalov H. C., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984 | MR | Zbl
[2] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Fizmatlit, M., 1993 | MR | Zbl
[3] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi silno neodnorodnykh uprugikh sred, Izd-vo Mosk. un-ta, M., 1990
[4] Pyatnitskii A. L., Chechkin G. A., Shamaev A. S., Usrednenie. Metody i nekotorye prilozheniya, Tamara Rozhkovskaya, Novosibirsk, 2007
[5] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR
[6] Frenkel Ya. I., “K teorii seismicheskikh i seismoelektricheskikh yavlenii vo vlazhnoi pochve”, Izv. AN SSSR. Ser. geogr. i geofiz., 1944
[7] Biot M. A., “Generalized theory of acoustic propagation in porous dissipative media”, J. Acoust. Soc. America, 34 (1962), 1254–1264 | DOI | MR
[8] Gilbert R. P., Mikelic A., “Homogenizing the acoustic properties of the seabed. Pt I”, Nonlinear Anal., 40 (2000), 185–212 | DOI | MR | Zbl
[9] Nguetseng G., “A general convergence result for a functional related to the theory of homogenization”, SIAM J. Math. Anal., 20:3 (1989), 608–623 | DOI | MR | Zbl
[10] Nguetseng G., “Asymptotic analysis for a staff variational problem arising in mathematics”, SIAM J. Math. Anal., 21:6 (1990), 1396–1414 | DOI | MR
[11] Kosmodemyanskii D. A., Shamaev A. S., “Spektralnye svoistva nekotorykh zadach mekhaniki silno neodnorodnykh sred”, Sovrem. matematika. Fundam. napravleniya, 17 (2006), 88–109
[12] Meiermanov A., “Metod dvukhmasshtabnoi skhodimosti Nguetsenga v zadachakh filtratsii i seismoakustiki v uprugikh poristykh sredakh”, Sib. mat. zhurn., 48:3 (2007), 645–667 | MR
[13] Shamaev A. S., Samarin V. A., “O rasprostranenii akusticheskikh voln v srede, sostoyaschei iz vyazkoi zhidkosti i uprugogo materiala”, Sovrem. matematika i ee prilozheniya, 35 (2005), 83–89 | MR
[14] Allaire G., “Homogenization and two-scale convergence”, SIAM J. Math. Anal., 23 (1992), 1482–1518 | DOI | MR | Zbl
[15] Allaire G., Damlamian A., Hornung U., “Two-scale convergence on periodic surfaces and applications”, Mathematical Modeling of Flow through Porous Media, eds. A. Bourgeat, C. Carasso, S. Luckhaus, A. Mikelic, Singapore, 1995, 15–25 | MR
[16] Lukassen D., Nguetseng G., Wall P., “Two-scale convergence”, Int. J. Pure Appl. Math., 20:1 (2002), 35–86 | MR
[17] Neuss-Radu M., “Some extension of two-scale convergence”, C. R. Acad. Sci. Paris. Sér. I, 322 (1996), 899–904 | MR | Zbl
[18] Zhikov V. V., “O dvukhmasshtabnoi skhodimosti”, Tr. seminara im. I. G. Petrovskogo, 23 (2003), 149–187 | MR | Zbl
[19] Zhikov V. V., “Ob odnom rasshirenii i primenenii metoda dvukhmasshtabnoi skhodimosti”, Mat. sb., 191:7 (2000), 31–72 | DOI | MR | Zbl
[20] Shulga C. B., “Usrednenie nelineinykh variatsionnykh zadach s pomoschyu dvukhmasshtabnoi skhodimosti”, Tr. MIRAN im. V. A. Steklova, 235, 2001, 1–8 | MR | Zbl
[21] Akulenko L. D., Nesterov S. V., “Dinamicheskaya model poristoi sredy, zapolnennoi vyazkoi zhidkostyu”, Dokl. RAN, 401:5 (2005), 630–633
[22] Akulenko L. D., Nesterov S. V., “Inertsionnye i dissipativnye svoistva poristoi sredy, zapolnennoi vyazkoi zhidkostyu”, Izv. RAN. MTT, 2005, no. 1, 109–119
[23] Akulenko L. D., Nesterov S. V., “Issledovanie inertsionnykh i uprugikh svoistv propitannykh zhidkostyu granulirovannykh sred rezonansnym metodom”, Izv. RAN. MTT, 2002, no. 5, 145–156
[24] Akulenko L. D., Nesterov S. V., “Uprugie svoistva granulirovannoi sredy, propitannoi zhidkostyu”, Izv. RAN. MTT, 2008, no. 1, 3–16
[25] Gurtin M. E., Pipkin A. C., “A general theory of heat conduction with finite wave speeds”, Arch. Rational Mech. Anal., 31 (1968), 113–126 | DOI | MR | Zbl
[26] Pandolfi L., “The controllability of the Gurtin–Pipkin equation: A cosine operator approach”, Appl. Math. Optim., 52 (2005), 143–165 | DOI | MR | Zbl
[27] Sanchez-Hubert J., “Asymptotic study of the macroscopic behavior of a solid-liquid mixture”, Math. Methods Appl. Sci., 2 (1980), 1–18 | DOI | MR
[28] Miloslavskii A. B., Spektralnye svoistva operatornogo puchka, voznikayuschego v vyazkouprugosti, Dep. v Ukr. VINITI 17.07.87. No 1225-87
[29] Vlasov V. V., Wu J., “Solvability and spectral analysis of abstract hyperbolic equations with delay”, J. Funct. Differential Equations, 16:4 (2009), 751–768 | MR | Zbl
[30] Vlasov V. V., Vu Dzh., “Spektralnyi analiz i razreshimost abstraktnykh giperbolicheskikh uravnenii s posledeistviem”, Differents. uravneniya, 45:4 (2009), 524–533 | MR | Zbl
[31] Vlasov V. V., Vu Dzh., Kabirova G. R., “Korrektnaya razreshimost i spektralnye svoistva abstraktnykh giperbolicheskikh uravnenii s posledeistviem”, Sovrem. matematika. Fundam. napravleniya, 35 (2010), 44–59 | MR | Zbl
[32] Vlasov V. V., Medvedev A. D., “Funktsionalno-differentsialnye uravneniya v prostranstvakh Soboleva i svyazannye s nimi voprosy spektralnoi teorii. I”, Sovrem. matematika. Fundam. napravleniya, 30 (2008), 3–173 | MR
[33] Palin V. V., Radkevich E. V., “Zakony sokhraneniya i ikh giperbolicheskie regulyarizatsii”, Sovremennye problemy matematiki i mekhaniki, v. 1, Differents. uravneniya, Izd-vo Mosk. un-ta, M., 2009
[34] Laptev V., Numerical Solution of Coupled Flow in Plain and Porous Media, PhD Thesis, University of Kaiserslautern, 2004
[35] Wesseling P., Principles of Computational Fluid Dynamics, Springer, 2001 | MR