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Regularized solution of an ill-posed biharmonic equation

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Abstract

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.

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Acknowledgements

We would like to thank the referees for their constructive comments and remarks.

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Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics Laboratory, University Badji Mokhtar, P.O. Box. 12, 23000, Annaba, Algeria

    S. Hamida

  2. Department of Mathematics, University of 8 Mai 1945, P.O. Box. 401, 24000, Guelma, Algeria

    A. Benrabah

  3. Applied Mathematics Laboratory, University Badji Mokhtar, P.O. Box. 12, 23000, Annaba, Algeria

    A. Benrabah

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  1. S. Hamida
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Hamida, S., Benrabah, A. Regularized solution of an ill-posed biharmonic equation. Rend. Circ. Mat. Palermo, II. Ser 70, 1709–1731 (2021). https://doi.org/10.1007/s12215-020-00584-5

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