Boundary value problems for a third order equation with multiple characteristics in three-dimensional space in semi-bounded domains

In this article, for a third-order equation with multiple characteristics, boundary value problems in three-dimensional space in semi-bounded domains are formulated and studied. The uniqueness of the solution is proven by the method of energy integrals. The existences of solutions is proved by the method of separation of variables. The solutions are constructed explicitly in the form of an infinite series, and the possibility of term-by-term differentiation of the series with respect to all variables is justified.