Infinite systems for a biharmonic problem in a rectangle

Abstract

Davis (2003) discussed non-uniqueness and solvability conditions of two types of infinite systems that occur in various biharmonic boundary-value problems for a rectangular domain studied by Meleshko & Gomilko (1997). This paper further elu-cidates the property of the non-uniqueness of the solution of infinite linear systems in a historical retrospective. It is shown that, in spite of the existence of non-unique solutions of homogeneous infinite systems, the physical quantities involved are always uniquely determined. Knowledge of asymptotic behaviour of unknowns is important when solving infinite systems by the method of reduction.