The criterion for the unique solvability of the Dirichlet and Poincare spectral problems for the multidimensional Euler-Darbo u x-Poisson equation

Abstract

In the cylindrical region of Euclidean space for the multi-dimensional Euler-Darbu-Poisson equation, the spectral problems of Dirichle and Poincare are considered. The solution is sought in the form of decomposition by multidimensional spherical functions. The theorem of existence and uniqueness of the classical solution has been proved. Conditions of unique solvability of the assigned tasks are obtained, which depend significantly on the height of the cylinder