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