科研之友
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摘要
In this paper, we consider a Cauchy problem for the semi-linear elliptic equation and use a modified boundary Tikhonov-type regularization method to overcome its ill-posedness. The existence, uniqueness and stability of the regularization solution are proven. Under an a-priori bound assumption for the exact solution, a convergence estimate of Holder type for this method is obtained. Finally, an iterative scheme is proposed to calculate the regularization solution, numerical results show that this method works well.
