Reports AIAS. Vol. 19, no 1. P. 22-30. ISSN 1726-9946

Contents of this issue

MATHEMATICS

Research Article

On the boundary conditions of the wave potential in a domain with a curviline borders

Kal’menov T.Sh.¹ – academician of AIAS, academician of NAS RK,

Derbissaly B.O.²

¹Institute of Mathematics and Mathematical Modeling, Almaty
²Al-Farabi Kazakh National University, Almaty
E-mail: ¹kalmenov.t@mail.ru, ²derbissaly@math.kz

   We study a one-dimensional volume wave potential in a domain with curvilinear boundaries. As a kernel of the wave potential we have chosen the fundamental solution of the Cauchy problem. It is well-known that in this case the volume wave potential satisfies one-dimensional initial conditions of Cauchy. We have constructed boundary conditions to which the wave potential satisfies at lateral boundaries of the domain. It is shown that the formulated initial-boundary value problem has the unique classical solution.

Keywords: wave equation, initial-boundary value problem, equation hyperbolic type, boundary condition, wave potential.

© T.Sh. Kal’menov,
B.O. Derbissaly, 2019

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For citation. Kal’menov T.Sh., Derbissaly B.O. On the boundary conditions of the wave potential in a domain with a curviline borders. Reports Adyghe (Circassian) International Academy of Sciences. 2019, vol. 19, no. 1, pp. 22-30.

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