Geodesic
Solvability of a Boundary-Value Problem with an Integral Boundary Condition of the Second Kind for Equations of Odd Order
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 163-172.

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

We study the solvability of a boundary-value problem for equations of odd order subject to a boundary condition relating the values of the conormal derivative with those of an integral operator applied to the solution. We prove the existence and uniqueness theorems for regular solutions.
Keywords: boundary-value problem, integral boundary condition of the second kind, differential operator, conormal derivative, Hölder's inequality, Young's inequality. 
@article{MZM_2010_88_2_a0,
     author = {A. M. Abdrakhmanov},
     title = {Solvability of a {Boundary-Value} {Problem} with an {Integral} {Boundary} {Condition} of the {Second} {Kind} for {Equations} of {Odd} {Order}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--172},
     publisher = {mathdoc},
     volume = {88},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a0/}
}
TY  - JOUR
AU  - A. M. Abdrakhmanov
TI  - Solvability of a Boundary-Value Problem with an Integral Boundary Condition of the Second Kind for Equations of Odd Order
JO  - Matematičeskie zametki
PY  - 2010
SP  - 163
EP  - 172
VL  - 88
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a0/
LA  - ru
ID  - MZM_2010_88_2_a0
ER  - 
%0 Journal Article
%A A. M. Abdrakhmanov
%T Solvability of a Boundary-Value Problem with an Integral Boundary Condition of the Second Kind for Equations of Odd Order
%J Matematičeskie zametki
%D 2010
%P 163-172
%V 88
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a0/
%G ru
%F MZM_2010_88_2_a0
A. M. Abdrakhmanov. Solvability of a Boundary-Value Problem with an Integral Boundary Condition of the Second Kind for Equations of Odd Order. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 163-172. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a0/

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

[2] L. I. Kamynin, “Ob odnoi kraevoi zadache teorii teploprovodimosti 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] A. Friedman, “Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions”, Quart. Appl. Math., 44:3 (1986), 401–407 | MR | Zbl

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

[6] N.-E. Benouor, A. Bouziani, “Problème mixte avec conditions intégrales pour une classe d'équations paraboliques”, C. R. Acad. Sci. Paris Sér. I Math., 321:9 (1995), 1177–1182 | MR | Zbl

[7] D. G. Gordeziani, G. A. Avalishvili, “Resheniya nelokalnykh zadach dlya odnomernykh kolebanii sredy”, Matem. modelirovanie, 12:1 (2000), 94–103 | MR | Zbl

[8] D. Gordeziani, G. Avalishvili, “Investigation of the nonlocal initial boundary value problem for some hyperbolic equations”, Hiroshima Math. J., 31:3 (2001), 345–366 | MR | Zbl

[9] L. S. Pulkina, “Smeshannaya zadacha s nelokalnym usloviem dlya giperbolicheskogo uravneniya”, Neklassicheskie uravneniya matematicheskoi fiziki, In-t matem. SO RAN, Novosibirsk, 2002, 176–184

[10] L. S. Pulkina, Nelokalnye zadachi dlya giperbolicheskikh uravnenii, Avtoreferat diss. $\dots$ dokt. fiz.-matem. nauk, Izd-vo Mosk. un-ta, M., 2003

[11] R. V. Shamin, “Nonlocal parabolic problems with the support of nonlocal terms inside a domain”, Funct. Differ. Equ., 10:1-2 (2003), 307–314 | MR | Zbl

[12] L. S. Pulkina, “Nelokalnaya zadacha s integralnymi usloviyami dlya giperbolicheskogo uravneniya”, Differents. uravneniya, 40:7 (2004), 887–892 | MR | Zbl

[13] A. Bouziani, “Initial-boundary value problem for a class of pseudoparabolic equations with integral boundary conditions”, J. Math. Anal. Appl., 291:2 (2004), 371–386 | DOI | MR | Zbl

[14] N. I. Ivanchov, “Kraevye zadachi dlya parabolicheskogo uravneniya s integralnymi usloviyami”, Differents. uravneniya, 40:4 (2004), 547–564 | MR | Zbl

[15] 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

[16] A. I. Kozhanov, L. S. Pulkina, “Kraevye zadachi s nelokalnym granichnym usloviem integralnogo vida dlya mnogomernykh giperbolicheskikh uravnenii”, Dokl. RAN, 404:5 (2005), 589–592 | MR | Zbl

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

[18] L. S. Pulkina, “Nachalno-kraevaya zadacha s nelokalnym granichnym usloviem dlya mnogomernogo giperbolicheskogo uravneniya”, Differents. uravneniya, 44:8 (2008), 1084–1089 | MR

[19] A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications, Oper. Theory Adv. Appl., 91, Birkhäuser Verlag, Basel, 1997 | MR | Zbl

[20] A. M. Nakhushev, Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006 | Zbl

[21] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR | Zbl

[22] I. E. Egorov, V. E. Fedorov, Neklassicheskie uravneniya matematicheskoi fiziki vysokogo poryadka, Izd-vo VTs SO RAN, Novosibirsk, 1995 | MR