A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations


In the present paper, we devote our effort to Cauchy boundary value problems for biharmonic equations. In general, the investigated problem is ill-posed. Therefore, we develop a filter method to defeat the ill-posedness of the problem. Explicit convergence rate is established under both a priori and a posteriori parameter choice rules. Finally, a numerical example is presented to illustrate the ill-posedness of the problem as well as the effectiveness of the proposed method.

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Correspondence to Tra Quoc Khanh.

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Luan, T.N., Khieu, T.T. & Khanh, T.Q. A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations. Numer Algor 86, 1721–1746 (2021). https://doi.org/10.1007/s11075-020-00951-4

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  • Biharmonic equation
  • Ill-posed problem
  • Filter method
  • Cauchy boundary value problem

Mathematics Subject Classification 2010

  • Primary 31B30
  • 47A52
  • 65F22
  • 65J20