The Third Boundary Problem for a Mixed-Type Equation with Three Singular Coefficients
Abstract
In this work, the third boundary value problem for a three-dimensional mixed-type equation with three singular coefficients in a domain consisting of a quarter cylinder and a rectangular triangular prism is studied. The existence and uniqueness of the formulated problem is proved by the method of spectral analysis. The solution of the considered problem is constructed as the sum of a double series. In substantiating the uniform convergence of the constructed series, asymptotic estimates for the Bessel functions of the real and imaginary arguments were used. Based on them, 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.