On solvability of a nonlocal problem with nonlinear integral condition for
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 12-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the solvability of a problem for a multidimensional w.r.t. spatial variables hyperbolic equation with a nonlinear integral condition on the lateral area. The unique solvability in the Sobolev space is proved. The proof is based on a priori estimates obtained in the article.
Keywords: nonlocal problem, integral condition, solvability.
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N. V. Beylina. On solvability of a nonlocal problem with nonlinear integral condition for. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 12-20. http://geodesic.mathdoc.fr/item/VSGU_2010_4_a1/

[1] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp.

[2] Kozhanov A. I., Pulkina L. S., “O razreshimosti kraevykh zadach s nelokalnym granichnym usloviem integralnogo vida dlya mnogomernykh giperbolicheskikh uravnenii”, Differents. uravneniya, 42:9 (2006), 1166–1179 | MR | Zbl

[3] Pulkina L. S., “Nelokalnaya zadacha s integralnym usloviem pervogo roda dlya mnogomernogo giperbolicheskogo uravneniya”, Doklady AN, 416:5 (2007), 590–597 | MR

[4] Dmitriev V. B., “Nelokalnaya zadacha s nelineinym integralnym usloviem dlya giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Fiz.-mat. nauki, 2009, no. 1(18), 26–32

[5] Beilin S. A., “Smeshannaya zadacha s integralnym usloviem dlya volnovogo uravneniya”, Neklassicheskie uravneniya matematicheskoi fiziki, Izd-vo In-ta matematiki, Novosibirsk, 2005, 37–43 | Zbl

[6] Pulkina L. S., “Smeshannaya zadacha s integralnym usloviem dlya giperbolicheskogo uravneniya”, Mat. zametki, 74:3 (2003), 435–445 | DOI | MR

[7] Pulkina L. S., “Smeshannaya zadacha s integralnym usloviem dlya giperbolicheskogo uravneniya”, Differents. uravneniya, 40:7 (2004), 887–892 | MR

[8] Chabakauri G. D., “Suschestvovanie i edinstvennost obobschennogo resheniya smeshannoi zadachi dlya volnovogo uravneniya s nelineinym nelokalnym granichnym usloviem”, Differents. uravneniya, 40:1 (2004), 77–81 | MR | Zbl

[9] Gording L., Zadacha Koshi dlya giperbolicheskikh uravnenii, Inostr. lit., M., 1961, 120 pp.

[10] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR