Geodesic
Averaging of operators with a~fine-scaled structure of boundary conditions
Matematičeskie zametki, Tome 65 (1999) no. 4, pp. 496-510.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{MZM_1999_65_4_a1,
     author = {A. Yu. Belyaev and G. A. Chechkin},
     title = {Averaging of operators with a~fine-scaled structure of boundary conditions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {496--510},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1999_65_4_a1/}
}
TY  - JOUR
AU  - A. Yu. Belyaev
AU  - G. A. Chechkin
TI  - Averaging of operators with a~fine-scaled structure of boundary conditions
JO  - Matematičeskie zametki
PY  - 1999
SP  - 496
EP  - 510
VL  - 65
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1999_65_4_a1/
LA  - ru
ID  - MZM_1999_65_4_a1
ER  - 
%0 Journal Article
%A A. Yu. Belyaev
%A G. A. Chechkin
%T Averaging of operators with a~fine-scaled structure of boundary conditions
%J Matematičeskie zametki
%D 1999
%P 496-510
%V 65
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1999_65_4_a1/
%G ru
%F MZM_1999_65_4_a1
A. Yu. Belyaev; G. A. Chechkin. Averaging of operators with a~fine-scaled structure of boundary conditions. Matematičeskie zametki, Tome 65 (1999) no. 4, pp. 496-510. http://geodesic.mathdoc.fr/item/MZM_1999_65_4_a1/

[1] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Fizmatlit, M., 1993 | Zbl

[2] Marchenko V. A., Khruslov E. Ya., Kraevye zadachi v oblastyakh s melkozernistoi granitsei, Naukova dumka, Kiev, 1974

[3] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984

[4] Belyaev A. G., “Usrednenie tretei kraevoi zadachi dlya uravneniya Puassona v oblasti s bystro ostsilliruyuschei granitsei”, Vestn. MGU. Ser. 1. Matem., mekh., 1988, no. 6, 63–66 | MR | Zbl

[5] Belyaev A. G., O singulyarnykh vozmuscheniyakh kraevykh zadach, Diss. ... k. f.-m. n., MGU, M., 1990

[6] Bouchitte G., Lidouh A., Michel J. C., Suquet P., Might Boundary Homogenization Help to Understand Friction?, SMR 719/9, Internat. Centre for Theoretical Physics, Trieste, 1993

[7] Bouchitte G., Lidouh A., Suquet P., “Homogénéisation de frontière pour la modélisation du contact entre un corps déformable non-linéaire et un corps rigide”, C. R. Acad. Sci. Paris. Sér. I. Math., 313 (1991), 967–972 | MR | Zbl

[8] Belyaev A. G., Mikheev A. G., Shamaev A. S., “Difraktsiya ploskoi volny na bystro ostsilliruyuschei poverkhnosti”, ZhVMiMF, 32:8 (1992), 1258–1272 | MR | Zbl

[9] Movchan A. B., Nazarov S. A., “Vliyanie malykh nerovnostei poverkhnosti na napryazhennoe sostoyanie tela i energeticheskii balans pri roste treschiny”, PMM, 55:5 (1991), 819–828 | MR | Zbl

[10] Oleinik O. A., Shamaev A. S., Yosifian G. A., Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992

[11] Pyatnitskii A. L., Chechkin G. A., “O zadache Neimana v oblastyakh s bystrym narastaniem ostsillyatsii granitsy”, UMN, 51:5 (1996), 166–167

[12] Sanchez-Palencia E., Homogenization Techniques for Composite Media, Springer, Berlin–New York, 1987 | Zbl

[13] Sanchez-Palencia E., Suquet P., “Friction and homogenization of a boundary”, Free Boundary Problems: Theory and Applications, eds. A. Fasano, M. Primicerio, Pitman, London, 1983, 561–571 | MR

[14] Chechkin G. A., Friedman A., Piatnitski A. L., The Boundary Value Problem in Domains with Very Rapidly Oscillating Boundary, INRIA Rapport de Recherche No. 3062 (Décembre 1996), Unité de Recherche, Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis, 1996

[15] Belyaev A. G., Chechkin G. A., Piatnitski A. L., Asymptotic Behavior of Solutions for Boundary Value Problems in a Perforated Domain with Oscillating Boundary, Publications du Laboratoire d'Analyse. No. R98 000 (July 1998), Université P. et M. Curie, CNRS, Paris, 1998

[16] Belyaev A. G., Pyatnitskii A. L., Chechkin G. A., “Asimptoticheskoe povedenie resheniya kraevoi zadachi v perforirovannoi oblasti s ostsilliruyuschei granitsei”, Sib. matem. zh., 39:4 (1998), 730–754 | MR | Zbl

[17] Butazzo G., Dal Maso G., Mosco U., Asymptotic Behavior for Dirichlet Problems in Domains Bounded by Thin Layers, Preprint di Matematica No. 2, Scuola Norm. Sup., Pisa, 1987

[18] Chechkin G. A., “Usrednenie kraevykh zadach s singulyarnym vozmuscheniem granichnykh uslovii”, Matem. sb., 184:6 (1993), 99–150 | MR | Zbl

[19] Chechkin G. A., “O kraevykh zadachakh dlya ellipticheskogo uravneniya vtorogo poryadka s ostsilliruyuschimi granichnymi usloviyami”, Neklassicheskie differentsialnye uravneniya v chastnykh proizvodnykh, IM SO AN SSSR, Novosibirsk, 1988, 95–104 | MR

[20] Chechkin G. A., “Ob asimptoticheskikh svoistvakh chastichno zakreplennoi membrany”, UMN, 44:4 (1989), 227

[21] Oleinik O. A., Chechkin G. A., “O kraevykh zadachakh dlya ellipticheskikh uravnenii s bystro menyayuschimsya tipom granichnykh uslovii”, UMN, 48:6 (1993), 163–164 | MR | Zbl

[22] Oleinik O. A., Chechkin G. A., “O kraevykh zadachakh dlya sistemy teorii uprugosti s bystro menyayuschimsya tipom granichnykh uslovii”, UMN, 49:4 (1994), 114

[23] Chechkin G. A., “Polnoe asimptoticheskoe razlozhenie resheniya kraevoi zadachi s bystro menyayuschimisya granichnymi usloviyami v sloe”, UMN, 48:4 (1993), 218–219 | MR

[24] Chechkin G. A., “O kolebaniyakh tel s kontsentrirovannymi massami, raspolozhennymi na granitse”, UMN, 50:4 (1995), 105–106 | MR

[25] Chechkin G. A., “Asimptoticheskoe razlozhenie resheniya kraevoi zadachi s bystro menyayuschimsya tipom granichnykh uslovii”, Tr. sem. im. I. G. Petrovskogo, 19, Izd-vo Mosk. un-ta, M., 1996, 323–337 | Zbl

[26] Belyaev A. G., Chechkin G. A., “Usrednenie smeshannoi kraevoi zadachi dlya operatora Laplasa v sluchae, kogda predelnaya zadacha nerazreshima”, Matem. sb., 186:4 (1995), 47–60 | MR | Zbl

[27] Oleinik O. A., Chechkin G. A., “O povedenii reshenii i sobstvennykh znachenii kraevykh zadach s bystro menyayuschimisya granichnymi usloviyami dlya sistemy teorii uprugosti”, Sovremennye problemy mekhaniki sploshnoi sredy, MP “Kniga”, Rostov-na-Donu, 1995, 167–172

[28] Chechkin G. A., Oleinik O. A., “On the asymptotics of solutions and eigenvalues of the boundary value problems with rapidly alternating boundary conditions for the system of elasticity”, Atti Accad. Naz. Lincei. Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9). Mat. Appl., 7:1 (1996), 5–15 | MR | Zbl

[29] Belyaev A. Yu., Kozlov S. M., “Usrednenie uravnenii Stoksa v sluchainoi perforirovannoi oblasti”, UMN, 48:4 (1993), 211–212

[30] Beliaev A. Yu., Kozlov S. M., “Darcy equation for random porous media”, Comm. Pure Appl. Math., 49:1 (1996), 1–34 | 3.0.CO;2-J class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[31] Chechkin G. A., Belyaev A. Yu., “Sluchainoe granichnoe usrednenie”, Mezhdunarodnaya konferentsiya “Funktsionalnye prostranstva, teoriya priblizhenii, nelineinyi analiz”, Tezisy dokl. (g. Moskva, 27 aprelya – 3 maya 1995 g.), M., 1995, 296–298

[32] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | Zbl

[33] Roitberg Ya. A., Sheftel Z. G., “Teorema o gomeomorfizmakh dlya ellipticheskikh sistem i ee prilozheniya”, Matem. sb., 78 (120):3 (1969), 446–472 | MR | Zbl

[34] Iosida K., Functional Analysis, Springer, New York, 1965

[35] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[36] Temam R., Uravnenie Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | Zbl