In this paper, one boundary value problem is posed and investigated for a third-order equation of a parabolichyperbolic type of the form с Lu 0 x y              in a concave hexagonal area with two lines of type change. Studies of elliptic-parabolic and parabolic-hyperbolic equations of the second order began in the 50-60 years of the last century. In 1959, I.M. Gelfand [1] pointed out the need for joint consideration of equations in one part of the domain of parabolic, and the other part of hyperbolic types. He gives an example related to the movement of gas in a channel surrounded by a porous medium: in the channel, the movement of gas is described by the wave equation, outside of it by the diffusion equation. Then, in the 70-80 years of the twentieth century, research began on equations of the third and high orders of the parabolic-hyperbolic type. Boundary value problems for such equations were posed and studied for the first time by T.D.Juraev [2] and his students [3]. Over the past time, research on boundary value problems for equations of the third and high orders of the parabolichyperbolic type has developed broadly, and is currently expanding in the areas of complication of equations and the scope of their consideration, as well as generalization of the problems of equations considered for them (for example, see [4], [5], [6] and etc.).

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