A Problem for a Three-Dimensional Equation of Mixed Type With Singular Coefficient

Abstract

In this paper, we study the spatial Tricomi problem for a three-dimensional equation of mixed type with a singular coefficient in a domain whose elliptical part is a quarter of a cylinder, and whose hyperbolic part is a triangular right prism. The study of the problem is carried out using the method of separation of variables and spectral analysis. The solution to the considered problem is constructed as a sum of a double series. To justify the uniform convergence of the constructed series, asymptotic estimates of the Bessel and Gauss functions were used. On their basis, estimates were obtained for each member of the series, which made it possible to prove the convergence of the resulting series and its derivatives up to the second order inclusive, as well as the existence theorem in the class of regular solutions.