Geodesic
The Tricomi problem for a third order hyperbolic equation degenerating inside the domain
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 67-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we study the Tricomi problem for a third-order hyperbolic equation with degeneracy of order inside a mixed domain. The existence and uniqueness theorem for a regular solution is proved.
Keywords: degenerate hyperbolic equation, Tricomi problem, fractional integro-differentiation operator.
Mots-clés : Hallaire equation 
@article{VKAM_2018_3_a7,
     author = {R. Kh. Makaova},
     title = {The {Tricomi} problem for a third order hyperbolic equation degenerating inside the domain},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {67--75},
     year = {2018},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_3_a7/}
}
TY  - JOUR
AU  - R. Kh. Makaova
TI  - The Tricomi problem for a third order hyperbolic equation degenerating inside the domain
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2018
SP  - 67
EP  - 75
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VKAM_2018_3_a7/
LA  - ru
ID  - VKAM_2018_3_a7
ER  - 
%0 Journal Article
%A R. Kh. Makaova
%T The Tricomi problem for a third order hyperbolic equation degenerating inside the domain
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2018
%P 67-75
%N 3
%U http://geodesic.mathdoc.fr/item/VKAM_2018_3_a7/
%G ru
%F VKAM_2018_3_a7
R. Kh. Makaova. The Tricomi problem for a third order hyperbolic equation degenerating inside the domain. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 67-75. http://geodesic.mathdoc.fr/item/VKAM_2018_3_a7/

[1] Hallaire M., “L'eau et la productions vegetable”, Institut National de la Recherche Agronomique, 9 (1964)

[2] Smirnov M. M., Vyrozhdayushchiesya giperbolicheskie uravneniya, Vyshehjshaya shkola, Minsk, 1977, 150 pp.

[3] Showalter R.E., Ting T.W., “Pseudoparabolic partial differential equations”, SIAM J. Math. Anal., 1:1 (1970), 1-26 | DOI | MR | Zbl

[4] CHudnovskij A.F., Teplofizika pochv, Nauka, M., 1976, 352 pp.

[5] Nahushev A.M., “Ob odnom klasse nagruzhennyh uravnenij v chastnyh proizvodnyh drobnogo poryadka”, Doklady Adygskoj (CHerkesskoj) Mezhdunarodnoj akademii nauk, 14:1 (2012), 51–57

[6] Coleman B. D., Duffin R. J., Mizel V. J., “Instability, Uniqueness, and Nonexistence Theorems for the Equation on a Strip”, Arch. Rat. Mech. Anal., 19 (1965), 100–116 | DOI | MR | Zbl

[7] Colton D., “Pseudoparabolic Equations in One Space Variable”, Journal of Differ. Equations, 12:3 (1972), 559–565 | DOI | MR | Zbl

[8] Shkhanukov M. Kh., “Some boundary value problems for a third-order equation that arise in the modeling of the filtration of a fluid in porous media”, Differential Equations, 18:4 (1982), 689–699 | MR | Zbl

[9] Yangarber V.A., “The mixed problem for a modified moisture-transfer equation”, Journal of Applied Mechanics and Technical Physics., 8:1 (1967), 62–64 | DOI

[10] Kozhanov A. I., “On a Nonlocal Boundary Value Problem with Variable Coefficients for the Heat Equation and the Aller Equation”, Differential Equations, 40:6 (2004), 815–826 | DOI | MR | Zbl

[11] Makaova R.H., “Vtoraya kraevaya zadacha dlya obobshchennogo uravneniya Allera s drobnoj proizvodnoj Rimana–Liuvillya”, Doklady Adygskoj (CHerkesskoj) Mezhdunarodnoj akademii nauk, 17:3 (2015), 35–38

[12] Nahushev A. M., Uravneniya matematicheskoj biologii, Vysshaya shkola, M., 1995, 301 pp.

[13] Nahushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp.

[14] Kal'menov T. Sh., “A criterion for the uniqueness of the solution of the Darboux problem for a certain degenerate hyperbolic equation”, Differential Equations, 7:1 (1971), 178–181 | MR | Zbl

[15] Kal'menov T. Sh., “The Darboux problem for a certain degenerate equation”, Differential Equations, 10:1 (1974), 59–68 | MR | Zbl

[16] Balkizov Zh. A., “The first boundary value problem for a degenerate hyperbolic equation”, Vladikavkaz. Mat. Zh., 18:2 (2016), 19–30 | MR

[17] Balkizov ZH.A., “Kraevaya zadacha dlya vyrozhdayushchegosya vnutri oblasti giperbolicheskogo uravneniya”, Izvestiya VUZov. Severo-Kavkazskij region. Seriya: Estestvennye nauki., 1:189 (2016), 5–10

[18] Repin O. A., Kraevye zadachi so smeshcheniem dlya uravnenij giperbolicheskogo i smeshannogo tipov., izdatel'stvo Saratovskogo universiteta, Saratov, 1992, 161 pp. | MR

[19] Nahushev A. M., Zadachi so smeshcheniem dlya uravnenij v chastnyh proizvodnyh, Nauka, M., 2006, 287 pp.

[20] Makaova R. Kh., “A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 21:4 (2017), 651–664 | Zbl

[21] Makaova R.H., “Kraevaya zadacha dlya vyrozhdayushchegosya vnutri oblasti giperbolicheskogo uravneniya tret'ego poryadka s operatorom Allera v glavnoj chasti”, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149:211 (2018), 64–71

[22] Pskhu A. V., “Initial-value problem for a linear ordinary differential equation of noninteger order”, Mat. Sb., 202:4 (2011), 111–122 | DOI | MR | Zbl

[23] Makaova R.H., “Pervaya kraevaya zadacha v nelokal'noj postanovke dlya obobshchennogo uravneniya Allera s drobnoj proizvodnoj Rimana - Liuvillya”, Vestnik AGU. Seriya 4: Estestvenno-matematicheskie i tekhnicheskie nauki, 4:211 (2017), 36–41