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In the present paper in a pentagonal domain a boundary-value problem was set and investigated for a third order parabolic hyperbolic equation in the form (b ∂ ∂y + с) (Lu) = 0 . Unique solvability of the considered problem was proved by the method of construct solution and also by methods of integral equations and differential equations, method of continuity.

INVESTIGATION OF A BOUNDARY-VALUE PROBLEM FOR A THIRD ORDER PARABOLIC HYPERBOLIC EQUATION IN THE FORM ?? ?? ???? +С ???? =?? .