On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation - Attaev, A.Kh. (Karagandy University of the name of acad. E.A. Buketov, 2023)
The work is devoted to the problem of setting new boundary and internal boundary value problems for hyperbolic equations. The consideration of these settings is given on the example of a wave equation. The research involves the d’Alembert method, the mean value theorem and the method of successive approximations. The paper formulates and studies a number o f non-local problems summarizing the classical Goursat and Dardu tasks. Some of them are marginal, and the other part is internal-marginal, and in both cases both characteristic and uncharacteristic displacements are considered. It should also be noted that a number of problems discussed below arose as a special case in the construction of the theory of correct problems for the model loaded equation of string oscillation.
Ішек тербелісінің теңдеуі үшін кейбір бейлокал шеттік және ішкі шеттік есептер
0 некоторых нелокальных краевых и внутренних краевых задачах для уравнения колебания струны
Keywords: Wave equation; general solution; Cauchy problem; Goursat problem; Darboux problem; problem with characteristic shift; problem with uncharacteristic displacement