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Regularized Solution of the Cauchy Problem for the Biharmonic Equation

  • Tran Nhat Luan
  • Tran Thi Khieu
  • Tra Quoc Khanh
Article
  • 17 Downloads

Abstract

In this paper, the Cauchy problem associated with the biharmonic equation is investigated. We prove that in principle, the problem is severely ill-posed in the sense of Hadamard. Therefore, we propose a quasi-boundary value-type regularization method for stabilizing the ill-posed problem. Very sharp convergence estimates are established based on some a priori information on the exact solution. Finally, several numerical examples with random data are provided to show the effectiveness of the proposed method.

Keywords

Biharmonic equation Fourth-order elliptic equation Cauchy problem Regularization method A posteriori parameter choice rule 

AMS Subject Classification

31B30 47A52 65F22 65J20 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Institute of Computational Science and TechnologyHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of Science, Ho Chi Minh City National UniversityHo Chi Minh CityVietnam
  3. 3.Division of Computational Mathematics and Engineering, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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