Geodesic
Asymptotic behaviour of solutions of a singular elliptic system
Sbornik. Mathematics, Tome 194 (2003) no. 1, pp. 31-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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A system of two conjugate elliptic equations with a small parameter at the highest derivatives is considered in a rectangle with two sides parallel to the characteristics of the limiting equations. The method of matched asymptotic expansions is used for the construction of uniform asymptotic series for solutions of this system up to an arbitrary power of the small parameter. 
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A. R. Danilin. Asymptotic behaviour of solutions of a singular elliptic system. Sbornik. Mathematics, Tome 194 (2003) no. 1, pp. 31-61. http://geodesic.mathdoc.fr/item/SM_2003_194_1_a2/

[1] Ilin A. M., Soglasovanie asimtoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[2] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR

[3] Danilin A. R., “Asimptotika upravlenii dlya singulyarnoi ellipticheskoi zadachi”, Dokl. AN, 369:3 (1999), 305–308 | MR | Zbl

[4] Danilin A. R., “Approksimatsiya singulyarno vozmuschennoi ellipticheskoi zadachi optimalnogo upravleniya”, Matem. sb., 191:10 (2000), 3–12 | MR | Zbl

[5] Kapustyan V. E., “Asimptotika ogranichennykh upravlenii v optimalnykh ellipticheskikh zadachakh”, Dokl. AN Ukrainy. Ser. matem., estestvozn., tekhn. nauki, 1992, no. 2, 70–74 | MR

[6] Danilin A. R., “Asimptotika ogranichennykh upravlenii dlya singulyarnoi ellipticheskoi zadachi v oblasti s maloi polostyu”, Matem. sb., 189:11 (1998), 27–60 | MR | Zbl

[7] Ilin A. M., Lelikova E. F., “Metod sraschivaniya asimptoticheskikh razlozhenii dlya uravnenii $\varepsilon\Delta u-a(x,y)u_y=f(x,y)$ v pryamougolnike”, Matem. sb., 119:3 (1982), 307–324 | MR | Zbl

[8] Lelikova E. F., “Metod sraschivaniya asimptoticheskikh razlozhenii dlya uravnenii $\varepsilon\Delta u-au_z=f$ v parallelepipede”, Differents. uravneniya, 14:9 (1978), 1638–1648 | MR | Zbl

[9] Kalyakin L. A., “Asimptotika resheniya sistemy dvukh lineinykh uravnenii MGD s singulyarnym vozmuscheniem. I. Standartnaya zadacha v ellipticheskom sloe”, Differents. uravneniya, 18:10 (1982), 1724–1738 | MR | Zbl

[10] Ilin A. M., “Pogranichnyi sloi”, Sovr. problemy matem. Fundament. napravleniya, 34, VINITI, M., 1988, 175–214

[11] Vasileva A. B., Dmitriev M. G., “Singulyarnye vozmuscheniya v zadachakh optimalnogo upravleniya”, Itogi nauki i tekhniki. Matem. analiz, 20, VINITI, M., 1982, 3–77 | MR

[12] Kokotovic P. V., “Application of singular perturbation techniques to control problems”, SIAM Rev., 26:4 (1984), 501–550 | DOI | MR | Zbl

[13] Lions J. L., Perturbations singulleres dans les problemes aux limites eten controle optimal, Lecture Notes in Math., 323, Springer-Verlag, Berlin, 1973 | MR | Zbl

[14] Lions J. L., “Asymptotic methods in the optimal control of distributed systems”, Automatica J. IFAC., 14 (1978), 199–211 | DOI | MR | Zbl

[15] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | Zbl

[16] Lebedev N. N., Spetsialnye funktsii i ikh prilozheniya, Fizmatgiz, M.-L., 1963 | MR

[17] Danilin A. R., “O razreshimosti odnoi sistemy uravnenii v chastnykh proizvodnykh”, Kompleksnyi analiz, differentsialnye uravneniya i smezhnye voprosy. II. Differentsialnye uravneniya, Trudy mezhdunarodnoi konferentsii, IM s VTs, Ufa, 2000, 53–57

[18] Karlsrou G. S., Teoriya teploprovodnosti, GITTL, M.–L., 1947