Geodesic
Gevrey Problem for a Loaded Mixed-Parabolic Equation with a Fractional Derivative
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 31-37.

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

In this paper, we consider the Gevrey problem for a loaded parabolic equation with the direct and reverse time in an unbounded region. The question on the solvability of this problem is reduced to the issue of the solvability of the generalized Abel equation in the class of function satisfying the Hölder condition.
Keywords: Gevrey problem, loaded equation, Riemann–Liouville fractional differentiation operator, function of Wright type, Hölder condition.
Mots-clés : Abel equation 
@article{INTO_2018_149_a3,
     author = {S. Kh. Gekkieva},
     title = {Gevrey {Problem} for a {Loaded} {Mixed-Parabolic} {Equation} with a {Fractional} {Derivative}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {31--37},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a3/}
}
TY  - JOUR
AU  - S. Kh. Gekkieva
TI  - Gevrey Problem for a Loaded Mixed-Parabolic Equation with a Fractional Derivative
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 31
EP  - 37
VL  - 149
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_149_a3/
LA  - ru
ID  - INTO_2018_149_a3
ER  - 
%0 Journal Article
%A S. Kh. Gekkieva
%T Gevrey Problem for a Loaded Mixed-Parabolic Equation with a Fractional Derivative
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 31-37
%V 149
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_149_a3/
%G ru
%F INTO_2018_149_a3
S. Kh. Gekkieva. Gevrey Problem for a Loaded Mixed-Parabolic Equation with a Fractional Derivative. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 31-37. http://geodesic.mathdoc.fr/item/INTO_2018_149_a3/

[1] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977

[2] Gekkieva S. Kh., “Zadacha Zhevre dlya smeshanno-parabolicheskogo uravneniya s drobnoi proizvodnoi”, Izv. Kabardino-Balkar. nauch. tsentra RAN, 76:2 (2017), 38–43

[3] Gekkieva S. Kh., “Smeshannye kraevye zadachi dlya nagruzhennogo diffuzionno-volnovogo uravneniya”, Nauch. vedomosti BelGU. Ser. Mat. Fiz., 42:6 (227) (2016), 32–35

[4] Zarubin E. A., “O edinstvennosti zadachi Zhevre dlya smeshannogo uravneniya diffuzii drobnogo poryadka”, Sovremennye metody v teorii kraevykh zadach, Voronezh. vesennyaya mat. shkola «Pontryaginskie chteniya–XV», Voronezh, 2004, 93–94

[5] Kerefov A. A., “Zadacha Zhevre dlya odnogo smeshanno-parabolicheskogo uravneniya”, Differ. ur-ya, 13:1 (1977), 76–83 | MR | Zbl

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

[7] Kislov N. V., Chervyakov A. V., “Kraevaya zadacha s menyayuschimsya napravleniem vremeni”, Vestn. MEI, 2002, no. 6, 62–67

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

[9] Nakhushev A. M., Nagruzhennye uravneniya i ikh primenenie, Nauka, M., 2012

[10] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995

[11] Popov S. V., “O pervoi kraevoi zadache dlya parabolicheskogo uravneniya s menyayuschimsya napravleniem vremeni”, Dinam. sploshnoi sredy, 102 (1991), 100–113 | Zbl

[12] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005

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

[14] Serbina L. I., Nelokalnye matematicheskie modeli perenosa v vodonosnykh sistemakh, Nauka, M., 2007

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

[16] Gevrey M., “Sur les equations aux derives partielles du type parabolique”, J. Math. App., 9:6 (1913), 305–475