S. Z. Djamalov, R. R. Ashurov, M. A. Sultanov, U. Sh. Ruziev, “On the unique solvability of a seminonlocal boundary value problem for the loaded Сhaplygin equation in a rectangle”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2020, Volume 31, Number 2,Pages <nobr>8

MATHEMATICS

On the unique solvability of a seminonlocal boundary value problem for the loaded Сhaplygin equation in a rectangle

S. Z. Djamalov^ab, R. R. Ashurov^b, M. A. Sultanov^c, U. Sh. Ruziev^a

^a Branch of the Russian State University of Oil and Gas (NRU) named after I. M. Gubkin in Tashkent
^b Institute of Mathematics named after V. I. Romanovskiy, Academy of Sciences of Uzbekistan
^c International Kazakh-Turkish University named after Khoja Ahmed Yasawi

Abstract: In this work, under certain conditions on the coefficients of the loaded Chaplygin equation in a rectangle, the unique solvability of a seminonlocal boundary value problem in Sobolev space is proved.

Keywords: loaded Chaplygin equation, seminonlocal boundary-value problem, the correctness of the solution, methods of "e-regularization", Galerkin's and successive approximations.

UDC: 517.956.6

MSC: Primary 35M10; Secondary 35M20

DOI: 10.26117/2079-6641-2020-31-2-8-17