Geodesic
A Problem with Integral Conditions for an Elliptic-Parabolic Equation
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 81-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

A problem with integral conditions for a differential equation of elliptic-parabolic type in a mixed domain consisting of a rectangle and a half-disk is posed. The unique solvability of this problem is proved.
Keywords: differential equation of mixed type, nonlocal problem, integral condition.
Mots-clés : elliptic-parabolic equation 
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A. K. Urinov; Sh. T. Nishonova. A Problem with Integral Conditions for an Elliptic-Parabolic Equation. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a8/

[1] J. R. Cannon, “The solution of the heat equation subject to the specification of energy”, Quart. Appl. Math., 21 (1963), 155–160 | DOI | MR | Zbl

[2] L. I. Kamynin, “Ob odnoi kraevoi zadache teorii teploprovodnosti s neklassicheskimi granichnymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 4:6 (1964), 1006–1024 | MR | Zbl

[3] N. I. Ionkin, “Reshenie odnoi kraevoi zadachi teorii teploprovodnosti s neklassicheskim kraevym usloviem”, Differents. uravneniya, 13:2 (1977), 294–304 | MR | Zbl

[4] L. A. Muravei, A. V. Filinovskii, “Ob odnoi nelokalnoi kraevoi zadache dlya parabolicheskogo uravneniya”, Matem. zametki, 54:4 (1993), 98–116 | MR | Zbl

[5] A. M. Nakhushev, Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995 | Zbl

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

[7] A. I. Kozhanov, L. S. Pulkina, “O razreshimosti nekotorykh granichnykh zadach so smescheniem dlya lineinykh giperbolicheskikh uravnenii”, Matem. zhurn., 9:2 (32) (2009), 78–92

[8] Ya. T. Megraliev, “O zadache identifikatsii lineinogo istochnika dlya ellipticheskogo uravneniya vtorogo poryadka s integralnym usloviem”, Tr. in-ta matem. NAN Belarusi, 21:2 (2013), 128–141

[9] L. S. Pulkina, A. E. Savenkova, “Zadacha s integralnym smescheniem dlya odnomernogo giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:2 (2016), 276–289 | DOI

[10] A. K. Urinov, Sh. T. Nishonova, “Zadachi s integralnym usloviem dlya uravnenii ellipticheskogo tipa”, Uzbekskii matem. zhurn., 2016, no. 2, 124–132

[11] A. Friedman, “Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions”, Quart. Appl. Math., 44:3 (1986), 401–407 | DOI | MR | Zbl

[12] T. Sh. Kalmenov, D. Suragan, “K spektralnym voprosam ob'emnogo potentsiala”, Dokl. RAN, 428:1 (2000), 16–19

[13] A. I. Kozhanov, “O razreshimosti kraevoi zadachi s nelokalnym granichnym usloviem dlya lineinykh parabolicheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 30, SamGTU, Samara, 2004, 63–69 | DOI

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

[15] L. S. Pulkina, A. E. Savenkova, “Zadacha s nelokalnym po vremeni usloviem dlya mnogomernogo giperbolicheskogo uravneniya”, Izv. vuzov. Matem., 2016, no. 10, 41–52

[16] O. S. Zikirov, “Ob odnoi zadache s integralnymi usloviyami dlya uravneniya tretego poryadka”, Uzbekskii matem. zhurn., 2006, no. 4, 26–31 | MR

[17] A. M. Abdurakhmanov, A. I. Kozhanov, “Zadacha s nelokalnym granichnym usloviem dlya odnogo klassa uravnenii nechetnogo poryadka”, Izv. vuzov. Matem., 2007, no. 5, 3–12 | MR | Zbl

[18] A. K. Urinov, K. S. Khalilov, “O nekotorykh neklassicheskikh zadachakh dlya odnogo klassa parabolo-giperbolicheskikh uravnenii”, Dokl. AMAN, 16:4 (2014), 42–49

[19] A. K. Urinov, K. S. Khalilov, “Nelokalnye zadachi s integralnym usloviem dlya parabolo-giperbolicheskogo uravneniya”, Dokl. AN RUz, 2014, no. 5, 8–10

[20] A. K. Urinov, A. O. Mamanazarov, “A problem with integral condition for a parabolic-hyperbolic equation with non-characteristic line of type changing”, Contemp. Anal. Appl. Math., 3:2 (2015), 170–183 | DOI | MR

[21] K. B. Sabitov, “Kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa s nelokalnym integralnym usloviem”, Differents. uravneniya, 46:10 (2010), 1468–1478 | MR | Zbl

[22] Yu. K. Sabitova, “Kraevaya zadacha s nelokalnym integralnym usloviem dlya uravnenii smeshannogo tipa s vyrozhdeniem na perekhodnoi linii”, Matem. zametki, 98:3 (2015), 393–406 | DOI | MR | Zbl

[23] T. D. Dzhuraev, Kraevye zadachi dlya uravnenii smeshannogo i smeshanno-sostavnogo tipov, Fan, Tashkent, 1979 | MR | Zbl

[24] A. K. Urinov, “Ob odnoi nelokalnoi kraevoi zadache dlya uravneniya Lavrenteva–Bitsadze”, Izv. AN UzSSR. Ser. fiz.-matem. nauk, 1988, no. 3, 36–42 | MR | Zbl

[25] M. S. Salakhitdinov, A. K. Urinov, “Zadachi tipa Bitsadze–Samarskogo dlya uravneniya smeshannogo tipa”, Dokl. AN SSSR, 317:5 (1991), 1058–1061 | MR | Zbl

[26] M. S. Salakhitdinov, M. Mirsaburov, Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, Universitet, Tashkent, 2005

[27] A. V. Bitsadze, Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR | Zbl

[28] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1965 | MR | Zbl

[29] V. I. Smirnov, Kurs vysshei matematiki, T. 4, Ch. 2, Nauka, M., 1981