Geodesic
On a nonlocal problem for nonlinear parabolic equation
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 42-49 
J. O. Takhirov; R. N. Turaev. On a nonlocal problem for nonlinear parabolic equation. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/VMJ_2014_16_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A boundary problem for nonlinear parabolic equation with nonlocal boundary conditions is considered. Some a priori estimates are derived to establish the global existence of the solution. Uniqueness and existence theorems are proved.

[1] Samarskii A. A., Mikhailov A. P., Matematicheskoe modelirovanie: Idei. Metody. Primery, Fizmatlit, M., 1997, 320 pp. | MR

[2] Samarskii A. A. i dr., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii parabolicheskikh uravnenii, Nauka, M., 1987, 477 pp. | MR

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

[4] Kruzhkov S. N., “Nelineinye parabolicheskie uravneniya s dvumya nezavisimymi peremennymi”, Tr. Mosk. matem. obsch-va, 16, 1967, 329–346 | MR | Zbl

[5] Kruzhkov S. N., “Kvazilineinye parabolicheskie uravneniya i sistemy s dvumya nezavisimymi peremennymi”, Tr. seminara im. I. G. Petrovskogo, 5, 1979, 217–272 | MR | Zbl

[6] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968, 428 pp.

[7] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985, 374 pp. | MR

[8] Khudyaev S. I., “Pervaya kraevaya zadacha dlya nelineinykh parabolicheskikh uravnenii”, Dokl. AN SSSR, 149:3 (1963), 535–538 | Zbl

[9] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 301 pp.