Cauchy problem for the Laplace equation in a radially symmetric hollow cylinder

Boundary value problems

Yun-Jie Ma¹  Chu-Li Fu² 

[1] School of Mathematics and Informational Science, Yantai University, Yantai, P.R. China;School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China

关键词: Cauchy problem for the Laplace equation;    hollow cylinder;    ill-posed problem;    regularization;    error estimates;    35R25;    35R30;   

DOI  :  10.1186/s13661-016-0702-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, an axisymmetric Cauchy problem for the Laplace equation in an unbounded hollow cylinder is considered. The Cauchy data are given on the inside surface of the cylinder, and the solution on the whole domain is sought. We propose a Fourier method with a priori and a posteriori parameter choice rules to solve this ill-posed problem. It is shown that the approximate solutions are stably convergent to the exact ones with explicit error estimates. A further comparison in the numerical aspects demonstrates the effectiveness and accuracy of the presented methods.

【 授权许可】

CC BY