Geodesic
On parabolic boundary value problems with a small parameter on the derivatives with respect to $t$
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 287-302 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Conditions are obtained of the type in Tikhonov's theorem which, when satisfied, make possible passage to the limit on the small parameter $\varepsilon$. Estimates in Hölder spaces of functions are obtained for the solution of the problem. The author determines how the rate of convergence of the solution to the limit function as $\varepsilon\to0$ depends on the smoothness of the functions contained in the equations and the boundary and initial conditions. Cases of both finite and infinite time intervals are considered. Bibliography: 14 titles. 
@article{SM_1988_59_2_a1,
     author = {V. G. Borisov},
     title = {On parabolic boundary value problems with a~small parameter on the derivatives with respect to~$t$},
     journal = {Sbornik. Mathematics},
     pages = {287--302},
     year = {1988},
     volume = {59},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/}
}
TY  - JOUR
AU  - V. G. Borisov
TI  - On parabolic boundary value problems with a small parameter on the derivatives with respect to $t$
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 287
EP  - 302
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/
LA  - en
ID  - SM_1988_59_2_a1
ER  - 
%0 Journal Article
%A V. G. Borisov
%T On parabolic boundary value problems with a small parameter on the derivatives with respect to $t$
%J Sbornik. Mathematics
%D 1988
%P 287-302
%V 59
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/
%G en
%F SM_1988_59_2_a1
V. G. Borisov. On parabolic boundary value problems with a small parameter on the derivatives with respect to $t$. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 287-302. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/

[1] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschikh malye parametry pri proizvodnykh”, Matem. sb., 31(73) (1952), 575–586 | Zbl

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR | Zbl

[3] Sayasov Yu. S., Vasileva A. B., “Obosnovanie i usloviya primenimosti metoda kvazistatsionarnykh kontsentratsii Semënova–Bodenshteina”, ZhFKh, 29 (1955), 802–810

[4] Butuzov V. F., “Asimptotika reshenii nekotorykh modelnykh zadach khimicheskoi kinetiki s uchetom diffuzii”, DAN SSSR, 242 (1978), 268–271 | MR | Zbl

[5] Butuzov V. F., Nesterov A. V., “Ob odnom singulyarno vozmuschennom uravnenii parabolicheskogo tipa”, Vestn. MGU. Ser. vychisl. matem. i kibern., 1978, no. 2, 49–56 | MR | Zbl

[6] Hoppensteadt F., “On quasilinear parabolic equations with a small parameter”, Comm. Pure and Appl. Math., 14 (1971), 17–38 | DOI | MR

[7] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981 | MR

[8] Borisov V. G., “Ob odnoi sisteme uravnenii parabolicheskogo tipa, soderzhaschei malyi parametr”, Dinamika sploshnoi sredy, 27, Novosibirsk, 1976, 23–32 | MR

[9] Borisov V. G., “O sisteme parabolicheskikh uravnenii, soderzhaschei malyi parametr pri proizvodnoi po vremeni”, Differents. uravneniya, 15 (1979), 1054–1058 | MR | Zbl

[10] Belonosov V. S., “Otsenki reshenii parabolicheskikh sistem v gelderovskikh klassakh s vesom”, DAN SSSR, 241 (1978), 265–268 | MR | Zbl

[11] Belonosov V. S., Vishnevskii M. P., “Ob ustoichivosti statsionarnykh reshenii nelineinykh parabolicheskikh sistem”, Matem. sb., 104(146) (1977), 534–558 | MR

[12] Solonnikov V. A., “O kraevykh zadachakh dlya lineinykh parabolicheskikh sistem differentsialnykh uravnenii obschego vida”, Tr. MIAN, 83 (1965) | MR

[13] Borisov V. G., Ob ustoichivosti reshenii kraevykh zadach dlya dvukh svyazannykh sistem uravnenii parabolicheskogo i ellipticheskogo tipov, Rukopis dep. v VINITI, No 3442-81 Dep. (Kemerovo, 1981)

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