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Regularized Solution of the Cauchy Problem for the Biharmonic Equation


Tran Nhat Luan, Tran Thi Khieu, Tra Quoc Khanh*

Source title: 
Bulletin of the Malaysian Mathematical Sciences Society, pp. 1-26, 2018 (ISI)
Academic year of acceptance: 

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.