On the Boundary Value Problem for a Three-Dimensional Analog of the Boussinesq Differential Equation

Abstract

This paper considers the questions of solvability and construction of the solution of the nonlocal boundary value problem for a three-dimensional analog of the homogeneous fourth-order Boussinesq differential equation. The spectral method is used based on separation of variables. The criterion of solvability of the considered problem is found. The solvability of the problem is proved under this criterion.

Keywords

• Boussinesq equation
• fourth-order equation
• three-dimensional domain
• integral condition
• solvability