BOUNDARY PROBLEMS AND EIGENVALUES OF THE GENERALIZED BIHARMONIC EQUATION,
Abstract
The solution of boundary value and eigenvalue problems for a generalized biharmonic equation is analyzed utilizing the P-transformation methods developed by G. N. Polozhii. Two kinds of boundary conditions are defined and five cases are distinguished. The five cases are: (1) on one side of a rectangle the boundary conditions of the first kind are satisfied and on the other sides the boundary conditions of the second kind are satisfied; (2) on two opposite sides the boundary conditions of the first kind and on the other sides the boundary conditions of the second kind are satisfied; (3) on two adjacent sides the boundary conditions of the first kind, and on the other sides the boundary conditions of the second kind are satisfied; (4) on three sides the boundary conditions of the first kind and on one side the boundary conditions of the second kind are satisfied; (5) on all sides the boundary conditions of the first kind are satisfied. The formula of summary representations, written in the scaler form, establishes the basis for solving the boundary-value and eigenvalue problems for all five cases of boundary conditions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 31, 1969
- Accession Number
- AD0687012
Entities
People
- B. N. Bublik
- G. N. Polozhii
Organizations
- National Air and Space Intelligence Center