Exact solutions of the Dirichlet – Neumann problem for the generalized Tricomi equation

Aim. The aim of the work is to find conditions under which the Tricomi equation has exact solutions and to find these solutions.

Methodology. We consider the Dirichlet – Neumann problem for a multidimensional generalization of the Tricomi equation in an infinite domain bounded by two hyperplanes. Using the Fourier transform, it is shown that this problem in the domain of ellipticity of the equation has a unique solution in the class of functions of slow growth.

Results. It is shown that when the right-hand sides of the equation and boundary conditions are polyharmonic functions (specifically, polynomials), exact solutions to the problem exist. An algorithm for obtaining the solution is presented.

Research implications consist of finding the conditions for the existence of exact solutions to the problem and finding the exact solutions themselves, which can be used to test the accuracy of approximate methods.

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