Title :
Optimal Wavelet Solutions for Ill-posed Elliptic Equations
Author :
Wang, Jin-ru ; Wang, Meng
Author_Institution :
Dept. of Appl. Math., Beijing Univ. of Technol., Beijing, China
Abstract :
In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip 0 ≤ × ≤ 1 is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it´s approximation is also provided.
Keywords :
Laplace equations; elliptic equations; 2D Laplace equation; Cauchy problem; Hermitian operator; Shannon wavelet bases; exact solution; ill-posed elliptic equations; ill-posed problem; optimal wavelet solutions; regularized solution; sharp stable estimates; spectral integral; Approximation methods; Equations; Laplace equations; Mathematical model; Vectors; Wavelet domain; Wavelet transforms; Convergence; Elliptic equation; Ill-posed problem; Wavelet;
Conference_Titel :
Chaos-Fractals Theories and Applications (IWCFTA), 2012 Fifth International Workshop on
Conference_Location :
Dalian
Print_ISBN :
978-1-4673-2825-8
DOI :
10.1109/IWCFTA.2012.11
