Modified nonlocal boundary value problem method for an ill-posed problem for the biharmonic equation.

In this paper, we propose a modified nonlocal boundary value problem method for an homogeneous biharmonic equation in a rectangular domain. We show that the considered problem is ill-posed in the sense of Hadamard, i.e. the solution does not depend continuously on the given data. Convergence estimates for the regularized solution are obtained under a priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]