A priori estimate of the solution of the analogue of the second boundary-value problem for the generalized third-order equation with short characteristics
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 20-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the boundary-value problem for a third-order equation of parabolic type with the fractional derivative of Caputo. By the method of energy inequalities an a priori estimate of the solution of the analogue of the second boundary value problem for an equation with multiple characteristics.
Keywords: A priori estimate of the boundary-value problems, equations with multiple characteristics, method of energy integrals, Caputo Fractional derivative.
@article{VKAM_2017_3_a2,
     author = {A. M. Shkhagapsoev},
     title = {A priori estimate of the solution of the analogue of the second boundary-value problem for the generalized third-order equation with short characteristics},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {20--24},
     year = {2017},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2017_3_a2/}
}
TY  - JOUR
AU  - A. M. Shkhagapsoev
TI  - A priori estimate of the solution of the analogue of the second boundary-value problem for the generalized third-order equation with short characteristics
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2017
SP  - 20
EP  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VKAM_2017_3_a2/
LA  - ru
ID  - VKAM_2017_3_a2
ER  - 
%0 Journal Article
%A A. M. Shkhagapsoev
%T A priori estimate of the solution of the analogue of the second boundary-value problem for the generalized third-order equation with short characteristics
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2017
%P 20-24
%N 3
%U http://geodesic.mathdoc.fr/item/VKAM_2017_3_a2/
%G ru
%F VKAM_2017_3_a2
A. M. Shkhagapsoev. A priori estimate of the solution of the analogue of the second boundary-value problem for the generalized third-order equation with short characteristics. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 20-24. http://geodesic.mathdoc.fr/item/VKAM_2017_3_a2/

[1] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, Moskva, 2003, 272 pp.

[2] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 668 pp. | MR

[3] Block H., “Sur les equations lineaires aux derivees partielles a carateristiques multiples”, Ark. mat., astron., fys, 7:13 (1912), 1–34

[4] Del Vecchio E., “Sulle equazioni $Z_{xxx}-Z_{y}+\varphi_1(x,y)=0$, $Z_{xxx}-Z_{yy}+\varphi_1(x,y)=0$”, Mem. Real acad. cienc. Torino., 66 (1915), 1–41 | Zbl

[5] Del Vecchio E., “Sulle deux problems d’integration pour las equazions paraboliques $Z_{xxx}-Z_y=0$, $Z_{xxx}-Z_{yy}=0$”, Ark. mat., astron., fys., 11 (1916), 32–34

[6] Cattabriga L., “Potenzialli di linia edi domino per equation nom paraboliche in olue variabli a caracteristiche multiple”, Rendi del Som. Mat. della Univ. di Padova., 3 (1961), 1–45 | MR

[7] Cattabriga L., “Un problema al kontorno per una equazione di ordine dispary”, Analli della scuola normale superior di pisa fis e mat., 3:2 (1959), 163–169 | MR

[8] Dzhuraev T. D., Kraevye zadachi dlya uravneniy smeshannogo i smeshanno-sostavnogo tipov, FAN, Tashkent, 1979, 236 pp. | MR

[9] Karova F. A., “Ustoychivost' i skhodimost' raznostnykh skhem, approksimiruyushchikh kraevye zadachi dlya uravneniya Allera s drobnoy proizvodnoy po vremeni”, Izvestiya KBNTs RAN, 2015, no. 3(65), 33–40

[10] Shkhagapsoev A. M., “A priori evaluation of the task of Cattabriga for the generalized third-order equation with multiple characteristics”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2016, no. 4-1(16), 66–71 | MR

[11] Shkhagapsoev A. M., “Apriornye otsenki resheniya kraevykh zadach dlya obobshchennogo uravneniya tret'ego poryadka s kratnymi kharakteristikami”, Izvestiya KBNTs RAN, 2016, no. 6(74), 96–101

[12] Caputo M., “Elasticita e Dissipazione”, Bologna (in Italian), 1969

[13] Alikhanov A. A., “Apriornye otsenki resheniy kraevykh zadach dlya uravneniy drobnogo poryadka”, Differentsial'nye uravneniya, 2010, no. 5(46), 658–664 | MR | Zbl