A Modified Tikhonov Regularization Method for a Cauchy Problem of the Biharmonic Equation

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.