ON A BOUNDARY VALUE PROBLEM OF THE TYPE OF THE TRICOMI PROBLEM FOR A MIXED SECOND-ORDER PARABOLIC-HYPERBOLIC EQUATION WITH THREE DISPLACEMENTS IN THE HYPERBOLIC PART OF THE DOMAIN

Author(s):  Zh.A. Balkizov, candidate of Sciences, Institute of Applied Mathematics and Automation KBSC RAS, Nalchik, Russia, Giraslan@yandex.ru

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  In this paper we study a boundary-value problem with a displacement for a nonhomogeneous equation of a mixed parabolic-hyperbolic type of the second order with a wave operator in the hyperbolicity region when the linear combination of the derivatives of the values of the desired function on two characteristics and on the line of change of type with variable coefficients is given as the boundary condition. Under a certain condition, the solution of the problem under study is explicitly written down on the coefficients in the statement of the problem. It is shown that if the above condition is violated by the coefficients, the homogeneous problem corresponding to the problem under study 1 has an infinite number of linearly independent solutions, and the solution set of the corresponding nonhomogeneous problem can exist only under an additional requirement on the given functions

Keywords:  boundary-value problem with displacement, equation of mixed parabolic-hyperbolic type, existence and uniqueness of the solution of the problem

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