Geodesic
Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder
Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 396-408.

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

In this paper, we consider a semilinear parabolic equation of second order with lower term a power function of the unknown function and prove that the sequence of solutions in a perforated cylinder tends to a solution in a unperforated cylinder if the radii of rejected balls in the parabolic metric tend to zero at the rate depending on the exponent of the power function in the lower term. 
@article{MZM_2005_78_3_a6,
     author = {H. Matevossian and I. V. Filimonova},
     title = {Homogenization of {Semilinear} {Parabolic} {Operators} in a {Perforated} {Cylinder}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {396--408},
     publisher = {mathdoc},
     volume = {78},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a6/}
}
TY  - JOUR
AU  - H. Matevossian
AU  - I. V. Filimonova
TI  - Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder
JO  - Matematičeskie zametki
PY  - 2005
SP  - 396
EP  - 408
VL  - 78
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a6/
LA  - ru
ID  - MZM_2005_78_3_a6
ER  - 
%0 Journal Article
%A H. Matevossian
%A I. V. Filimonova
%T Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder
%J Matematičeskie zametki
%D 2005
%P 396-408
%V 78
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a6/
%G ru
%F MZM_2005_78_3_a6
H. Matevossian; I. V. Filimonova. Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder. Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 396-408. http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a6/

[1] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978 | MR

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

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

[4] Brézis H., Friedman A., “Nonlinear parabolic equations involving measures as initial conditions”, J. Math. Pures Appl. (9), 62:1 (1983), 73–97 | MR | Zbl

[5] Brézis H., Peletier L. A., Terman D., “A very singular solution of the heat equation with absorption”, Arch. Rat. Mech. Anal., 95:3 (1986), 185–209 | DOI | Zbl

[6] Kamin S., Peletier L. A., “Singular solutions of the heat equation with absorption”, Proc. Amer. Math. Soc., 95:2 (1985), 205–210 | DOI | Zbl

[7] Ilin A. M., Oleinik O. A., Kalashnikov A. S., “Lineinye uravneniya vtorogo poryadka parabolicheskogo tipa”, UMN, 17:3 (1962), 3–146

[8] Matevosyan O. A., Pikulin S. V., “Ob usrednenii slabonelineinykh divergentnykh ellipticheskikh operatorov v perforirovannom kube”, Matem. zametki, 68:3 (2000), 390–398 | MR

[9] Matevosyan O. A., Pikulin S. V., “Ob usrednenii polulineinykh ellipticheskikh operatorov v perforirovannykh oblastyakh”, Matem. sb., 193:3 (2002), 101–114 | MR | Zbl

[10] Kondratev V. A., Landis E. M., “O kachestvennykh svoistvakh reshenii odnogo nelineinogo uravneniya vtorogo poryadka”, Matem. sb., 135:3 (1988), 346–360

[11] Chistyakov V. V., “O svoistvakh reshenii polulineinykh parabolicheskikh uravnenii vtorogo poryadka”, Tr. sem. im. I. G. Petrovskogo, 15, Izd-vo Mosk. un-ta, M., 1991, 70–107 | Zbl

[12] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[13] Nash J., “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., 80 (1958), 931–954 ; Нэш Дж., “О непрерывности решений параболических и эллиптических уравнений”, Математика, 4:1 (1960), 31–52 | DOI | Zbl

[14] Aronson D. G., “Bounds for the fundamental solution of a parabolic equation”, Bull. Amer. Math. Soc., 73 (1967), 890–896 | DOI | Zbl

[15] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | Zbl