Geodesic
Stabilization of the norm of the solution of a mixed problem
Sbornik. Mathematics, Tome 195 (2004) no. 3, pp. 413-440 
F. Kh. Mukminov; I. M. Bikkulov. Stabilization of the norm of the solution of a mixed problem. Sbornik. Mathematics, Tome 195 (2004) no. 3, pp. 413-440. http://geodesic.mathdoc.fr/item/SM_2004_195_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The behaviour as $t\to\infty$ of the solution of a mixed problem for parabolic equations in an unbounded domain with two exits to infinity is studied. A certain class of domains is distinguished, in which an estimate characterizing the stabilization of solutions and determined by the geometry of the domain is established. This estimate is proved to be sharp in a certain sense for a broad class of domains with two exits to infinity.

[1] Guschin A. K., “Ob otsenkakh reshenii kraevykh zadach dlya parabolicheskikh uravnenii vtorogo poryadka”, Trudy MIAN, 126, 1973, 5–45 | MR | Zbl

[2] Guschin A. K., “Stabilizatsiya reshenii vtoroi kraevoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 101 (143):4 (1976), 459–499 | MR | Zbl

[3] Guschin A. K., “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119 (161):4 (1982), 451–508 | MR

[4] Guschin A. K., Mikhailov V. P., “O stabilizatsii resheniya zadachi Koshi dlya odnomernogo parabolicheskogo uravneniya”, Trudy MIAN, 112, 1971, 181–202 | MR | Zbl

[5] Ushakov V. I., “Stabilizatsiya reshenii tretei smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka v netsilindricheskoi oblasti”, Matem. sb., 111 (153):1 (1980), 95–115 | MR | Zbl

[6] Guschin A. K., Mikhailov V. P., Mikhailov Yu. A., “O ravnomernoi stabilizatsii resheniya vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 128(170) (1985), 147–168 | MR | Zbl

[7] Bogoyavlenskii O. B., Vladimirov V. C., Volovich I. V., Guschin A. K., Drozhzhinov Yu. N., Zharinov V. V., Mikhailov V. P., “Kraevye zadachi matematicheskoi fiziki”, Trudy MIAN, 175, 1986, 63–102 | MR | Zbl

[8] Tedeev A. F., “Stabilizatsiya reshenii pervoi smeshannoi zadachi dlya kvazilineinogo parabolicheskogo uravneniya vysokogo poryadka”, Differents. uravneniya, 25:3 (1989), 491–498 | MR | Zbl

[9] Mukminov F. Kh., “Ob ubyvanii normy resheniya smeshannoi zadachi dlya parabolicheskogo uravneniya vysokogo poryadka”, Differents. uravneniya, 23:10 (1987), 1172–1780 | MR

[10] Mukminov F. Kh., “Stabilizatsiya reshenii pervoi smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 111 (153):4 (1980), 503–521 | MR | Zbl

[11] Vishik M. I., “Cmeshannye kraevye zadachi i priblizhennyi metod ikh resheniya”, Dokl. AN SSSR, 97:2 (1954), 193–196 | MR | Zbl

[12] Bers L., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966 | MR | Zbl

[13] Guschin A. K., “Nekotorye svoistva obobschennogo resheniya vtoroi kraevoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 97 (139) (1975), 242–261 | MR | Zbl

[14] Mukminov F. Kh., Stabilizatsiya reshenii pervoi smeshannoi zadachi dlya sistemy uravnenii Nave–Stoksa, Dis. ... dokt. fiz.-matem. nauk, MIRAN, M., 1994

[15] Kozhevnikova L. M., Mukminov F. Kh., “Otsenki skorosti stabilizatsii pri $t\to\infty$ reshenii pervoi smeshannoi zadachi dlya kvazilineinoi sistemy parabolicheskikh uravnenii vtorogo poryadka”, Matem. sb., 191:2 (2000), 91–131 | MR | Zbl

[16] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Fizmatgiz, M., 1961