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Nguyen Huy Tuan, Tran Thanh Binh; A Regularization Method for the Elliptic Equation with Inhomogeneous Source; Hindawi publishing, Vol. 2014 (2014), Article ID 525636, pp. 1 – 9 (Journal Paper).
We consider the following Cauchy problem for the elliptic equation with inhomogeneous source in a rectangular domain with Dirichlet boundary conditions at and . The problem is ill-posed. The main aim of this paper is to introduce a regularization method and use it to solve the problem. Some sharp error estimates between the exact solution and its regularization approximation are given and a numerical example shows that the method works effectively.