Regularized solution of an ill-posed biharmonic equation. (English) Zbl 1530.47012
Summary: In this paper we consider a severely ill posed problem associated with a two dimensional homogeneous biharmonic equation. By perturbing the original problem and using a two parameters regularization method, we get a stable solution which converges to the solution of the considered problem. Under some priori bound assumptions, different errors estimates for the regularized solution are obtained. These last ones depend on the choice of the space of the exact solution. To show the effectiveness of the proposed regularization method some numerical results are given.
MSC:
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
| 74K20 | Plates |
| 31A25 | Boundary value and inverse problems for harmonic functions in two dimensions |
Keywords:
ill-posed problems; two-parameter regularisation; biharmonic equation; plates; boundary value problems; inverse problemsReferences:
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