Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2020_32_4_a0, author = {M. A. Dorodnyi and T. A. Suslina}, title = {Homogenization of the hyperbolic equations with periodic coefficients in ${\mathbb R}^d$: {Sharpness} of the results}, journal = {Algebra i analiz}, pages = {3--136}, publisher = {mathdoc}, volume = {32}, number = {4}, year = {2020}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2020_32_4_a0/} }
TY - JOUR AU - M. A. Dorodnyi AU - T. A. Suslina TI - Homogenization of the hyperbolic equations with periodic coefficients in ${\mathbb R}^d$: Sharpness of the results JO - Algebra i analiz PY - 2020 SP - 3 EP - 136 VL - 32 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2020_32_4_a0/ LA - ru ID - AA_2020_32_4_a0 ER -
%0 Journal Article %A M. A. Dorodnyi %A T. A. Suslina %T Homogenization of the hyperbolic equations with periodic coefficients in ${\mathbb R}^d$: Sharpness of the results %J Algebra i analiz %D 2020 %P 3-136 %V 32 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/AA_2020_32_4_a0/ %G ru %F AA_2020_32_4_a0
M. A. Dorodnyi; T. A. Suslina. Homogenization of the hyperbolic equations with periodic coefficients in ${\mathbb R}^d$: Sharpness of the results. Algebra i analiz, Tome 32 (2020) no. 4, pp. 3-136. http://geodesic.mathdoc.fr/item/AA_2020_32_4_a0/
[1] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984 | MR
[2] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic analysis for periodic structures, Stud. Math. Appl., 5, North-Holland Publ. Co., Amsterdam-New York, 1978 | MR | Zbl
[3] Birman M. Sh., Suslina T. A., “Periodicheskie differentsialnye operatory vtorogo poryadka. Porogovye svoistva i usredneniya”, Algebra i analiz, 15:5 (2003), 1–108
[4] Birman M. Sh., Suslina T. A., “Porogovye approksimatsii rezolventy faktorizovannogo samosopryazhennogo semeistva s uchetom korrektora”, Algebra i analiz, 17:5 (2005), 69–90
[5] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh ellipticheskikh differentsialnykh operatorov s uchetom korrektora”, Algebra i analiz, 17:6 (2005), 1–104
[6] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh differentsialnykh operatorov s uchetom korrektora. Priblizhenie reshenii v klasse Soboleva $H^1(\mathbb{R}^d)$”, Algebra i analiz, 18:6 (2006), 1–130
[7] Birman M. Sh., Suslina T. A., “Operatornye otsenki pogreshnosti pri usrednenii nestatsionarnykh periodicheskikh uravnenii”, Algebra i analiz, 20:6 (2008), 30–107
[8] Conca C., Orive R., Vanninathan M., “Bloch approximation in homogenization and applications”, SIAM J. Math. Anal., 33:5 (2002), 1166–1198 | DOI | MR | Zbl
[9] Dorodnyi M. A., Operator error estimates for homogenization of the nonstationary Schrödinger-type equations: sharpness of the results, 2020, arXiv: 2005.06516 | Zbl
[10] Dorodnyi M. A., “Usrednenie periodicheskikh uravnenii tipa Shredingera pri vklyuchenii chlenov mladshego poryadka”, Algebra i analiz, 31:6 (2019), 122–196 | MR
[11] Dorodnyi M. A., Suslina T. A., “Usrednenie giperbolicheskikh uravnenii”, Funkts. anal. i ego pril., 50:4 (2016), 91–96 | MR | Zbl
[12] Dorodnyi M. A., Suslina T. A., “Spectral approach to homogenization of hyperbolic equations with periodic coefficients”, J. Differential Equations, 264:12 (2018), 7463–7522 | DOI | MR | Zbl
[13] Vasilevskaya E. S., “Usrednenie parabolicheskoi zadachi Koshi s periodicheskimi koeffitsientami pri uchete korrektora”, Algebra i analiz, 21:1 (2009), 3–60 | MR
[14] Vasilevskaya E. S., Suslina T. A., “Porogovye approksimatsii faktorizovannogo samosopryazhennogo operatornogo semeistva s uchetom pervogo i vtorogo korrektorov”, Algebra i analiz, 23:2 (2011), 102–146 | MR
[15] Vasilevskaya E. S., Suslina T. A., “Usrednenie parabolicheskikh i ellipticheskikh periodicheskikh operatorov v $L_2 (\mathbb{R}^d)$ pri uchete pervogo i vtorogo korrektorov”, Algebra i analiz, 24:2 (2012), 1–103 | MR
[16] Zhikov V. V., “Spektralnyi podkhod k asimptoticheskim zadacham diffuzii”, Differ. uravneniya, 25:1 (1989), 44–50 | MR | Zbl
[17] Zhikov V. V., “Ob operatornykh otsenkakh v teorii usredneniya”, Dokl. RAN, 403:3 (2005), 305–308 | MR | Zbl
[18] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Fizmatlit, M., 1993
[19] Zhikov V. V., Pastukhova S. E., “On operator estimates for some problems in homogenization theory”, Russ. J. Math. Phys., 12:4 (2005), 515–524 | MR | Zbl
[20] Zhikov V. V., Pastukhova S. E., “Estimates of homogenization for a parabolic equation with periodic coefficients”, Russ. J. Math. Phys., 13:2 (2006), 224–237 | DOI | MR | Zbl
[21] Zhikov V. V., Pastukhova S. E., “Ob operatornykh otsenkakh v teorii usredneniya”, Uspekhi mat. nauk, 71:3 (2016), 27–122 | MR | Zbl
[22] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972
[23] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR
[24] Mazya V. G., Shaposhnikova T. O., Multiplikatory v prostranstvakh differentsiruemykh funktsii, Izd. LGU, Leningrad, 1986 | MR
[25] Meshkova Yu. M., “Usrednenie zadachi Koshi dlya parabolicheskikh sistem s periodicheskimi koeffitsientami”, Algebra i analiz, 25:6 (2013), 125–177 | MR
[26] Meshkova Yu. M., “On operator error estimates for homogenization of hyperbolic systems with periodic coeffcients”, J. Spectr. Theory (to appear)
[27] Meshkova Yu. M., “Ob usrednenii periodicheskikh giperbolicheskikh sistem”, Mat. zametki, 105:6 (2019), 937–942 | MR | Zbl
[28] Meshkova Yu. M., “Usrednenie periodicheskikh parabolicheskikh sistem po $L_2(\mathbb{R}^d)$-norme pri uchete korrektora”, Algebra i analiz, 31:4 (2019), 137–197 | MR
[29] Meshkova Yu. M., Variations on the theme of the Trotter–Kato theorem for homogenization of periodic hyperbolic systems, 2019, arXiv: 1904.02781 | MR
[30] Pakhnin M. A., Suslina T. A., “Operatornye otsenki pogreshnosti pri usrednenii ellipticheskoi zadachi Dirikhle v ogranichennoi oblasti”, Algebra i analiz, 24:6 (2012), 139–177 | MR
[31] Sevostyanova E. V., “Asimptoticheskoe razlozhenie resheniya ellipticheskogo uravneniya vtorogo poryadka s periodicheskimi bystro ostsilliruyuschimi koeffitsientami”, Mat. sb., 115:2 (1981), 204–222 | MR | Zbl
[32] Suslina T. A., “Ob usrednenii periodicheskikh parabolicheskikh sistem”, Funkts. analiz i ego pril., 38:4 (2004), 86–90 | MR | Zbl
[33] Suslina T. A., “Homogenization of a periodic parabolic Cauchy problem”, Amer. Math. Soc. Transl. (2), 220, Amer. Math. Soc., Providence, RI, 2007, 201–233 | DOI | MR | Zbl
[34] Suslina T. A., “Homogenization of a periodic parabolic Cauchy problem in the Sobolev space $H^1(\mathbb{R}^d)$”, Math. Model. Nat. Phenom., 5:4 (2010), 390–447 | DOI | MR | Zbl
[35] Suslina T. A., “Usrednenie v klasse Soboleva $H^1(\mathbb{R}^d)$ dlya periodicheskikh ellipticheskikh differentsialnykh operatorov vtorogo poryadka pri vklyuchenii chlenov pervogo poryadka”, Algebra i analiz, 22:1 (2010), 108–221
[36] Suslina T. A., “Usrednenie ellipticheskikh sistem s periodicheskimi koeffitsientami: operatornye otsenki pogreshnosti v $L_2(\mathbb{R}^d)$ s uchetom korrektora”, Algebra i analiz, 26:4 (2014), 195–263
[37] Suslina T. A., “Spectral approach to homogenization of nonstationary Schrödinger-type equations”, J. Math. Anal. Appl., 446:2 (2017), 1466–1523 | DOI | MR | Zbl