Geodesic
On solvability of nonlocal problem for third-order equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 15-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper nonlocal problem with integral conditions for partial differential equation of the third order is considered. The existence of a unique classical solution is proved in rectangular domain. The proof is carried out by the method of auxiliary problems. At first the problem for a new function for partial differential equation of the first order is considered. Then the solvability of integral analogue of Goursat problem for hyperbolic equation of the second order is proved by equivalent reduction of the problem to the Volterra integral equation of the second kind.
Keywords: nonlocal problem, partial differential equation of the third order, integral conditions. 
@article{VSGU_2017_1_a1,
     author = {O. M. Ketchina},
     title = {On solvability of nonlocal problem for third-order equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {15--20},
     year = {2017},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_1_a1/}
}
TY  - JOUR
AU  - O. M. Ketchina
TI  - On solvability of nonlocal problem for third-order equation
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2017
SP  - 15
EP  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSGU_2017_1_a1/
LA  - ru
ID  - VSGU_2017_1_a1
ER  - 
%0 Journal Article
%A O. M. Ketchina
%T On solvability of nonlocal problem for third-order equation
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2017
%P 15-20
%N 1
%U http://geodesic.mathdoc.fr/item/VSGU_2017_1_a1/
%G ru
%F VSGU_2017_1_a1
O. M. Ketchina. On solvability of nonlocal problem for third-order equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 15-20. http://geodesic.mathdoc.fr/item/VSGU_2017_1_a1/

[1] Pulkina L. S., “On solvability of $L_{2}$ nonlocal problem with integral conditions for a hyperbolic equation”, Differential Equations, 2000, no. 2, 279–280 (in Russian)

[2] Zhegalov V. I.. Utkina E. A., “On one pseudoparabolic equation of the third order”, Russian Mathematics. (Iz. VUZ), 1999, no. 10, 73–76 (in Russian)

[3] Utkina E. A., “About uniqueness of the solution of semi-integral problem for one equation of the fourth order”, Vestnik of Samara State University. Natural Science Series, 2010, no. 4(78), 98–102 (in Russian)

[4] Utkina E. A., “Characteristic boundary-value problem for a third-order equation with pseudo-parabolic operator and with shifted arguments of desired function”, Russian Mathematics. (Iz. VUZ), 2014, no. 2, 54–60 (in Russian)

[5] Mironov A. N., Mironova L. B., “On Laplace invariants for equations with dominating third-order partial derivative and two independent variables”, Mathematical Notes, 99:1 (2016), 89–96 (in Russian) | DOI

[6] Mironov A. N., Mironova L. B., “Laplace invariants for a fourth-order equation with two independent variables”, Russian Mathematics. (Iz. VUZ), 2014, no. 10, 27–34 (in Russian)

[7] Asanova A. T., “Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle”, Russian Mathematics. (Iz. VUZ), 2017, no. 5, 11–25 (in Russian)

[8] Asanova A. T., “On a nonlocal problem with integral offset for hyperbolic systems of equations with mixed derivative”, Mathematical Journal, 8:1 (2008), 9–16 (in Russian)

[9] Beshtokov M. Kh., “A priori estimates of solutions of nonlocal boundary value problems for a pseudo-parabolic equation”, Vladikavkaz Mathematical Journal, 15:3 (2013), 19–36 (in Russian)

[10] Lukina G. A., “Boundary value problems with integral conditions for the third order equations”, Yakutian Mathematical Journal, 17:2 (2010), 75–97 (in Russian) | Zbl

[11] Kozhanov A. I., Popov N. S., “On solvability of some problems with displacement for pseudoparabolic equations”, Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 100:3 (2010), 46–62 (in Russian)

[12] Filippov A. F., Introduction to the theory of differential equations, Textbook, KomKniga, M., 2007, 240 pp. (in Russian)

[13] Nakhusheva Z. A., “On a nonlocal problem for partial differential equations”, Differential Equations, 1986, no. 1, 171–174 (in Russian)

[14] Pul'kina L. S., Ketchina O. M., “Nonlocal problem with integral conditions for a hyperbolic equation in characteristic rectangular”, Vestnik of Samara State University. Natural Science Series, 2009, no. 2(68), 80–88 (in Russian)

[15] Mikhlin S. G., Lectures on linear integral equations, Fizmatgiz, M., 1959, 232 pp. (in Russian)