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This article presents findings on boundary value problems in three-dimensional space, suggesting effective methods for solution existence and uniqueness.
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.
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Apakov et al. (2025) studied this question.
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