Geodesic
On the solvability of a boundary value problem for quasi-linear system equations of mixed and composite type in a multidimensional domain
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 2, pp. 46-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quasi-linear system of mixed-composite type with changing time direction in multidimensional domain is studied. The existence and uniqueness of generalized and regular solutions of boundary value problem are proved in weighted Sobolev space. 
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M. A. Nurmamedov. On the solvability of a boundary value problem for quasi-linear system equations of mixed and composite type in a multidimensional domain. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 2, pp. 46-61. http://geodesic.mathdoc.fr/item/VMJ_2010_12_2_a4/

[1] Tricomi F. G., “Sulle equazional lineari alle derivate parzialli di secondo ordinee, di tipo snisto”, Atti Accad. Naz. Lincei., 14 (1923), 133–247 | Zbl

[2] Frankl F. I., “On the problems of Chapligin for mixed subsonic and supersonic flows”, Izv. Akad. Nauk USSR. Ser. Math., 9:2 (1945), 121–143 | MR | Zbl

[3] Bers L., “Results and conjectures in the mathematical theory of subsonic and transonic gaz flows”, Comm. on Pure and Appl. Math., 7:1 (1954), 79–104 | DOI | MR | Zbl

[4] Bers L., Mathematical aspects of subsonic and transonic gas dynamics, Wiley, New York, 1958, 180 pp. | MR | Zbl

[5] Frankl F. I., Izbrannye trudy po gazovoi dinamike, Nauka, M., 1973, 711 pp. | MR

[6] Pini B., “Un problema di valori al contorno por un'equazional a derivative puzziali del terzo ordinee con parto principale di tipo composito”, Rend. Sem. Fus. Sci. Univ.—Cagliari, 27 (1957), 114–135 | MR

[7] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972, 587 pp. | MR

[8] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971, 372 pp. | Zbl

[9] Berazinski Yu. M., Expansion of eigenvalues functions for self-adjoint operators, Naukova Dumka, Kiev, 1965, 800 pp.

[10] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950, 255 pp. | MR

[11] Vragov V. N., Kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, Izd-vo Novosibirskogo gos. un-ta, Novosibirsk, 1983, 84 pp.

[12] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973, 576 pp. | MR

[13] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 408 pp. | MR

[14] Nurmamedov M. A., “Ob odnoi zadache dlya vyrozhdayuschegosya kvazilineinogo uravneniya smeshannogo tipa”, Neklassicheskie uravneniya matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1986, 175–178 | MR

[15] Nurmamedov M. A., “Pervaya kraevaya zadacha dlya uravneniya smeshannogo tipa vysokogo poryadka s menyayuschimsya napravleniem vremeni”, Tez. dokl. Vtorogo Sibirskogo kongressa po prikl. i industr. mat-ke, IM SO RAN, Novosibirsk, 1996, 93

[16] Nurmamedov M. A., “On the theory of well-posed boundary value problems for degenerating nonlinear equation mixed type with changing time direction”, Sakarya Math. Symposium, Turkey, 1997, 74

[17] Nurmamedov M. A., “Kraevye zadachi dlya kvazilineinogo uravneniya smeshannogo tipa s neskolkimi ploskostyami vyrozhdeniya”, Nelineinye problemy mat. fiziki, Dokl. VI respubl. konf., Donetsk, 1986, 104 | MR | Zbl

[18] Nurmamedov M. A., “Nekotorye korrektnye postanovki kraevykh zadach dlya uravnenii smeshannogo tipa s menyayuschimsya napravleniem vremeni”, Neklassicheskie uravneniya matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1987, 161–169

[19] Dubinskii Yu. A., “Kvazilineinye ellipticheskie i parabolicheskie uravneniya lyubogo poryadka”, Uspekhi mat. nauk, 23:1 (1968), 45–90 | MR | Zbl

[20] Morawetz C. S., “A weak solution for a system of equation of elliptic-hyperbolic type”, Comm. on Pure and Appl. Math., 9:1 (1955), 45–68 ; 10:1 (1957), 107–131 ; 11:1 (1958), 129–144 | DOI | MR | DOI | MR | Zbl | DOI | MR

[21] Morawetz C. S., “Mixed equations and transonic flow”, J. Hyperbolic Differ. Equat., 1 (2004), 1–26 | DOI | MR | Zbl

[22] Canic S., Keyfitz B. L., Kim E. H., “Mixed hyperbolic-elliptic systems in self-similar flows”, Bulletin Brazilian Math. Soc., 32 (2001), 377–399 | DOI | MR | Zbl

[23] Smirnov M. M., Vyrozhdayuschiesya ellipticheskie i giperbolicheskie uravneniya, Nauka, M., 1966, 292 pp. | MR

[24] Vragov V. N., “K teorii kraevykh zadach dlya uravnenii smeshannogo tipa”, Differents. uravneniya, 13:6 (1977), 1098–1105 | MR | Zbl

[25] Keldysh M. V., “O sobstvennykh znacheniyakh i sobstvennykh funktsiyakh nekotorykh klassov nesamosopryazhennykh uravnenii”, Dokl. AN SSSR, 77:2 (1951), 11–14 | MR | Zbl

[26] Fikera G., “K edinoi teorii kraevykh zadach elliptiko-parabolicheskikh uravnenii vtorogo poryadka”, Sb. perevodov. Matematika, 7:6 (1963), 99–121