Geodesic
Gevrey problem for a mixed parabolic equation with singular coefficients
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 18-29.

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

In this paper, we examine the unique solvability of the Gevrey problem for a mixed parabolic equation with singular coefficients in a band. We prove the existence and uniqueness of a solution to the problem stated. The uniqueness of a solution is proved by the method of energy integrals and the existence by methods of the theory of Volterra, Fredholm, and singular integral equations.
Keywords: Gevrey problem, mixed parabolic equation, uniqueness of solution
Mots-clés : singular coefficient, existence of solution. 
@article{INTO_2018_156_a1,
     author = {A. O. Mamanazarov},
     title = {Gevrey problem for a mixed parabolic equation with singular coefficients},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {18--29},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a1/}
}
TY  - JOUR
AU  - A. O. Mamanazarov
TI  - Gevrey problem for a mixed parabolic equation with singular coefficients
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 18
EP  - 29
VL  - 156
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_156_a1/
LA  - ru
ID  - INTO_2018_156_a1
ER  - 
%0 Journal Article
%A A. O. Mamanazarov
%T Gevrey problem for a mixed parabolic equation with singular coefficients
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 18-29
%V 156
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_156_a1/
%G ru
%F INTO_2018_156_a1
A. O. Mamanazarov. Gevrey problem for a mixed parabolic equation with singular coefficients. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 18-29. http://geodesic.mathdoc.fr/item/INTO_2018_156_a1/

[1] Akbarova M. Kh., Nelokalnye kraevye zadachi dlya parabolicheskikh uravnenii smeshannogo tipov, Avtoref. na soisk. uch. step. kand. fiz.-mat. nauk, Tashkent, 1995

[2] Beitmen G., Erdeii A., Vysshie trantsendentnye funktsii. Funktsiya Besselya. Funktsiya parabolicheskogo tsilindra. Ortogonalnye polinomy, Nauka, M., 1966

[3] Beitmen G., Erdeii A., Vysshie trantsendentnye funktsii. Gipergeometricheskaya Funktsiya. Funktsiya Lezhandra, Nauka, M., 1965

[4] Bers L., Matematicheskie voprosy dozvukovoi i okolozvukovoi gazovoi dinamiki, IL, M., 1961

[5] Bitsadze A. V., Uravneniya smeshannogo tipa, AN SSSR, M., 1959

[6] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1959

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

[8] Egorov I. E., “Ob odnoi kraevoi zadache dlya sistemy singulyarnykh parabolicheskikh uravnenii”, Dinamika sploshnoi sredy, v. 14, Novosibirsk, 1973, 100–105

[9] Kerefov A. A., “Ob odnoi kraevoi zadache Zhevre dlya parabolicheskogo uravneniya so znakoperemennym razryvom pervogo roda u koeffitsienta pri proizvodnoi po vremeni”, Differ. uravn., 10:1 (1974), 69–77 | MR | Zbl

[10] Kogan M. A, “O magnitogidrodinamicheskikh techeniyakh smeshannogo tipa”, Prikl. mat. mekh., 25:1 (1961), 132–157

[11] Kumyshev R. M., Suramova Zh. Kh., Sabanchieva A. A., Bitova A. A., “Kraevaya zadacha dlya smeshanno-parabolicheskogo uravneniya v ogranichennoi oblasti s menyayuschimsya napravleniem vremeni”, Akt. vopr. sovr. nauki, 2015, no. 2 (6), 4–8

[12] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR

[13] Polyanin A. D., Spravochnik po lineinym uravneniyam matematicheskoi fiziki, Fizmatlit, M., 2001

[14] Popov S. V., “Bezuslovnaya razreshimost pervoi kraevoi zadachi dlya singulyarnogo parabolicheskogo uravneniya s menyayuschimsya napravleniem vremeni”, Kraevye zadachi dlya neklassicheskikh uravnenii mat. fiziki, Novosibirsk, 1989, 153–160

[15] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987

[16] Tersenov S. A., Pervaya kraevaya zadacha dlya uravneniya parabolicheskogo tipa s menyayuschimsya napravleniem vremeni, Novosibirsk, 1978

[17] Tersenov S. A., Parabolicheskie uravneniya s menyayuschimsya napravleniem vremeni, Nauka, Novosibirsk, 1985

[18] Frankl F. I., “O bokovom vodozabore iz bystrykh melkikh rek”, Tr. Kirgiz. gos. un-ta, 2 (1953), 33–45

[19] Frankl F. I., Izbrannye trudy po gazovoi dinamike, Nauka, M., 1973

[20] Shopolov N. N., “Edna granichna zadacha za smeseno parabolichno uravnenie s nelokalni nachalni usloviya”, God. VUZ. Prilozh. mat., 15:2 (1980 (1981)), 7

[21] Gevrey M., “Sur les equations aux derivees partielles du type parabolique”, J. Math. Appl., 9 (1913), 305–475

[22] Gevrey M., “Sur les equations aux derivees partielles du type parabolique”, J. Math. Appl., 1914, 105–137

[23] Pagani C. D., Talenti G., “On an forward-backward parabolic equation”, Ann. Mat. Pura Appl., 90:4 (1971), 1–58 | DOI | MR

[24] Pagani C. D., “On the parabolic equation and a related one”, Ann. Mat. Pura Appl., 99:4 (1974), 333–399 | DOI | MR | Zbl