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2009•Journal of Jiamusi UniversityRequires access

Tikhonov Regularization Method for the Cauchy Problem of the Laplace Equation

Hongwu Zhang

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Abstract

In this paper,a Cauchy problem for the Laplace equation is considered in a rectangle domain.Cauchy data are given at y=0,and the boundary data are given at x=0 and x=π.The solution for 0y≤1 is sought.It is know that such problem is severely ill-posed.The authors use Tikhonov regularization method to solve it.Convergence estimations are presented under an a-priori boundary assumption for the exact solution.

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In this paper,a Cauchy problem for the Laplace equation is considered in a rectangle domain.Cauchy data are given at y=0,and the boundary data are given at x=0 and x=π.The solution for 0y≤1 is sought.It is know that such problem is severely ill-posed.The authors use Tikhonov regularization method to solve it.Convergence estimations are presented under an a-priori boundary assumption for the exact solution.

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Available abstract

In this paper,a Cauchy problem for the Laplace equation is considered in a rectangle domain.Cauchy data are given at y=0,and the boundary data are given at x=0 and x=π.The solution for 0y≤1 is sought.It is know that such problem is severely ill-posed.The authors use Tikhonov regularization method to solve it.Convergence estimations are presented under an a-priori boundary assumption for the exact solution.

Key concepts: Tikhonov regularization, Cauchy's convergence test, Cauchy problem, Rectangle, Mathematics, Regularization (linguistics), Cauchy boundary condition, Laplace's equation

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