Geodesic
The well-posedness of the Dirichlet and Poincare problems in a cylindric domain for the multi-dimensional Chapligin equation
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 3-10 
S. A. Aldashev. The well-posedness of the Dirichlet and Poincare problems in a cylindric domain for the multi-dimensional Chapligin equation. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 3-10. http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper proves the unique solvability of the Dirichlet and Poincare problems in a cylindric domain for the multi-dimensional Chapligin equation.

[1] Hadamard J., “Sur les problemes aux derivees partielles et leur signification physique”, Princeton University Bulletin, 13 (1902), 49–52 | MR

[2] Bitsadze A. V., Uravneniya smeshannogo tipa, Izd. AN SSSR, M., 1959, 164 pp.

[3] Nakhushev A. M., Zadachi so smescheniem dlya uravneniya v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp. | Zbl

[4] Bourgin D. G., Duffin R., “The Dirichlet problem the vibrating string eguation”, Bull. Amer. Math. Soc., 45 (1939), 851–858 | DOI | MR | Zbl

[5] Fox D. W., Pucci C., “The Dirichlet problem the wave eguation”, Ann. Math. Pura Appl., 46 (1958), 155–182 | DOI | MR | Zbl

[6] Nakhushev A. M., “Kriterii edinstvennosti zadachi Dirikhle dlya uravneniya smeshannogo tipa v tsilindricheskoi oblasti”, Dif. uravneniya, 6:1 (1970), 190–191 | Zbl

[7] Dunninger D. R., Zachmanoglou E. C., “The condition for uniqueness of the Diriclet problem for hyperbolic equations in cilindrical domains”, J. Math. Mech., 18:8 (1969), 763–766 | MR | Zbl

[8] Aldashev S. A., “The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation”, Math. Problems Engineering, 2010 (2010), Article ID 653215, 7 pp. | DOI | MR | Zbl

[9] Aldashev S. A., “The well-posedness of the Poincare problem in a cylindrical domain for the higher-dimensional wave equation”, J. of Math. Science, 173:2 (2011), 150–154 | DOI | MR | Zbl

[10] Mikhlin S. G., Mnogomernye singulyarnye integraly i integralnye uravneniya, Fizmatgiz, M., 1962, 254 pp. | MR

[11] Aldashev S. A., Kraevye zadachi dlya mnogomernykh giperbolicheskikh i smeshannykh uravnenii, Gylym, Almaty, 1994, 170 pp.

[12] Aldashev S. A., Vyrozhdayuschiesya mnogomernye giperbolicheskie uravneniya, ZKATU, Oral, 2007, 139 pp.

[13] Tersenov S. A., Vvedenie v teoriyu uravnenii, vyrozhdayuschikhsya na granitse, NGU, Novosibirsk, 1973, 139 pp. | MR

[14] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1985, 301 pp.

[15] Aldashev S. A., “Spektralnye zadachi Darbu–Prottera dlya odnogo klassa mnogomernykh giperbolicheskikh uravnenii”, Ukrainskii mat. zhurn., 55:1 (2003), 100–107 | MR | Zbl

[16] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1965, 703 pp. | MR

[17] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1974, 295 pp. | MR

[18] Smirnov V. I., Kurs vysshei matematiki, v. 4, ch. 1, Nauka, M., 1974, 334 pp. | MR

[19] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966, 724 pp. | MR

[20] Aldashev S. A., “Zadacha Dirikhle v tsilindricheskoi oblasti dlya mnogomernogo uravneniya Gellerstedta”, Materialy II Mezhdunar. Rossiisko-Kazakhskogo simpoziuma “Uravneniya smeshannogo tipa i rodstvennye problemy analiza i informatiki”, NII PM i KBNTs RAN, Nalchik, 2011, 21–22