Geodesic
Parametrized integral manifolds of singularly perturbed systems in the critical case for problems of chemical kinetics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1640-1653.

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

A constructive algorithm is proposed for calculating the coefficients of the asymptotic expansion of a slow motions integral manifold represented in parametric form. The existence and uniqueness theorem is proven for a parametrized integral manifold of a singularly perturbed system in a degenerate case.
Keywords: asymptotic expansion, integral manifold, singularly perturbed system, slow motions. 
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L. I. Kononenko. Parametrized integral manifolds of singularly perturbed systems in the critical case for problems of chemical kinetics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1640-1653. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a104/

[1] N.N. Bogolybov, Yu.A. Mitropol'skij, Asimptoticheskie metody v teorii kolebanij, Fizmatgiz, M., 1958

[2] Yu.A. Mitropol'skij, O.B. Lykova, Integral'nye mnogoobrazija v nelinejnoj mekhanike, Nauka, M., 1973

[3] A.B. Vasil'eva, V.F. Butuzov, Asimptoticheskie razlozhenija reshenij singuljarno vozmushchennykh uravnenij, Nauka, M., 1973

[4] E.F. Mishchenko, N.Kh. Rozov, Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija, Nauka, M., 1975

[5] K.V. Zadiraka, “O nelokal'nom integral'nom mnogoobrazii nereguljarno vozmushchennoj differencial'noj sistemy”, Ukrain. Mat. Zh., 17:1 (1965), 47–63 | DOI | Zbl

[6] Ja.S. Baris, V.I. Fodchuk, “Issledovanie ogranichennykh reshenij nelinejnykh nereguljarno vozmushchennykh sistem metodom integral'nykh mnogoobrazij”, Ukrain. Mat. Zh., 22:1 (1970), 3–11 | DOI | Zbl

[7] A.M. Samojlenko, “Invariantnye toroidal'nye mnogoobrazija sistem s medlenno menjajushchimisja peremennymi”, Problemy asimptoticheskoj teorii nelinejnykh kolebanij, Naukova dumka, Kiev, 1977, 181–191

[8] V.V. Strygin, V.A. Sobolev, Integral'nye mnogoobrazija i razdelenie dvizhenij, Izd-vo Kujbyshev, Un-ta, Kujbyshev, 1983 | MR

[9] V.M. Gol'dshtejn, V.A. Sobolev, Kachestvennyj analiz singuljarno vozmushchennykh sistem, Institut matematiki SO AN SSSR, Novosibirsk, 1988

[10] A.B. Vasil'eva, V.F. Butuzov, Singuljarno vozmushchennye uravnenija v kriticheskikh sluchajakh, Izd-vo MGU, M., 1978

[11] L.I. Kononenko, Integral'nye mnogoobrazija v matematicheskoj modeli reakcii okislenija kataliticheskogo okislenija, No 13, AN SSSR. Sib. otd-nie In-t matematiki, Novosibirsk, 1990 | Zbl

[12] V.M. Gol'dshtejn, L.I. Kononenko, M.Z. Lazman, V.A. Sobolev, G.S. Jablonskij, “Kachestvennyj analiz dinamicheskikh svojstv katalicheskogo izometricheskogo reaktora ideal'nogo smeshenija”, Matematicheskie problemy khimimcheskoj kinetiki, Sb. nauch. trudov, Nauka Sib. ot-nie, Novosibirsk, 1989, 176–204 | Zbl

[13] Zhongmei Gu, N. N. Nefedov, R.E. O'Malley, jr., “On singularsingularity perturbed initial value problem”, SIAM J. Appl. Math., 49:1 (1989), 1–25 | DOI | MR | Zbl

[14] V.M. Orlov, “Uproshchenie singuljarno vozmushchennykh uravnenij makro dinamiki i metod kvazistacionarnykh koncentracij”, ZhVM, 25:4 (1985), 521–534