Title :
Fourier Regularization Methods for the Cauchy Problem of an Elliptic Equation with Variable Coefficients
Author :
Qian, Ailin ; Mao, Jianfeng
Author_Institution :
Sch. of Math. & Stat., Xianning Univ., Xianning, China
Abstract :
In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Within the framework of general regularization theory, we present Fourier regularization method to stabilize the problem. Moreover, Holder-type stability error estimate is proved for this regularization method. According to the regularization theory, the error estimates are order optimal. Some numerical results are reported.
Keywords :
Fourier transforms; elliptic equations; partial differential equations; Cauchy problem; Fourier regularization methods; Holder-type stability error estimation; elliptic equation; general regularization theory; variable coefficients; Equations; Fourier transforms; Heating; Laplace equations; Noise level; Noise measurement; Numerical stability; Elliptic equation; Error estimate; Fourier regularization; Inverse problems;
Conference_Titel :
Intelligent System Design and Engineering Application (ISDEA), 2012 Second International Conference on
Conference_Location :
Sanya, Hainan
Print_ISBN :
978-1-4577-2120-5
DOI :
10.1109/ISdea.2012.671
