Geodesic
Solvability of the Cauchy problem for the Aller equation in space of bounded continuous functions
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 65-75 
Kh. G. Umarov. Solvability of the Cauchy problem for the Aller equation in space of bounded continuous functions. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 65-75. http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Solvability of the Cauchy problem for Aller differential equation is reduced to the abstract Cauchy problem in Banach space of bounded continuous functions on the real axis.

[1] Chudnovskii A. F., Teplofizika pochv, Nauka, M., 1976, 352 pp.

[2] Nakhushev A. M., “O nekotorykh sposobakh linearizatsii uravnenii dvizheniya gruntovykh vod i pochvennoi vlagi”, Kraevye zadachi dlya uravnenii smeshannogo tipa i rodstvennye problemy funktsionalnogo analiza i prikladnoi matematiki, 2, KBGU, Nalchik, 1979, 173–183

[3] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 301 pp. | Zbl

[4] Soldatov A. P., Shkhanukov M. Kh., “Kraevye zadachi s obschim nelokalnym usloviem A. A. Samarskogo dlya psevdoparabolicheskikh uravnenii vysokogo poryadka”, Dokl. AN SSSR, 297:3 (1987), 547–552 | MR

[5] Kozhanov A. I., “Ob odnoi nelokalnoi kraevoi zadache s peremennymi koeffitsientami dlya uravneniya teploprovodnosti i Allera”, Dif. uravneniya, 40:6 (2004), 763–774 | MR | Zbl

[6] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Izd-vo inostr. lit-ry, M., 1962, 895 pp.

[7] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967, 464 pp. | MR

[8] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971, 104 pp. | MR

[9] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966, 500 pp. | MR | Zbl

[10] Lyusternik L. A., Sobolev V. I., Kratkii kurs funktsionalnogo analiza, Vyssh. shkola, M., 1982, 271 pp. | MR | Zbl

[11] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer-Verlag, N.Y., 1983, 279 pp. | DOI | MR | Zbl

[12] Appell J., Zabreiko P. P., Nonlinear Superposition Operators, Cambridge Univ. Press, Cambridge, 1990, 320 pp. | MR | Zbl

[13] Filatov A. N., Sharova L. V., Integralnye neravenstva i teoriya nelineinykh kolebanii, Nauka, M., 1976, 152 pp. | MR | Zbl