A Modified Tikhonov Regularization Method for a Cauchy Problem of the Biharmonic Equation
Received:April 21, 2023  Revised:January 08, 2024
Key Words: Biharmonic equations   inverse problem   Cauchy problem   Tikhonov regularization method  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.1961044).
Author NameAffiliation
Fan YANG School of Science, Lanzhou University of Technology, Gansu 730050, P. R. China 
Jianming XU School of Science, Lanzhou University of Technology, Gansu 730050, P. R. China 
Xiaoxiao LI School of Science, Lanzhou University of Technology, Gansu 730050, P. R. China 
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Abstract:
      In this paper, the Cauchy problem of biharmonic equation is considered. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. Firstly, we give the conditional stability result under the a priori bound assumption for the exact solution. Secondly, a modified Tikhonov regularization method is used to solve this ill-posed problem. Under the a priori and the a posteriori regularization parameter choice rule, the error estimates between the regularization solutions and the exact solution are obtained. Finally, some numerical examples are presented to verify that our method is effective.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.03.008
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