Regularized Solution of the Cauchy Problem for the Biharmonic Equation
Regularized Solution of the Cauchy Problem for the Biharmonic Equation
Source title:
Bulletin of the Malaysian Mathematical Sciences Society, pp. 1-26,
2018
(ISI)
Academic year of acceptance:
2018-2019
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.