A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
-
Hongwu Zhang
and
Ting Wei
Abstract.
In this paper, a Cauchy problem for a semi-linear elliptic equation is considered. This problem is well known to be severely ill-posed and regularization methods are required. We use a Fourier truncated regularization method to deal with it, and a convergence estimate for the regularized solution is obtained under an a-priori bound assumption for the exact solution. Some numerical results are given to show the effectiveness of truncated method.
Funding source: NSF of China
Award Identifier / Grant number: 10971089
Funding source: NSF of China
Award Identifier / Grant number: 11171136
Funding source: YTSRF of Hexi University
Award Identifier / Grant number: QN2011-10
The author would like to thank the reviewers for their constructive comments and valuable suggestions that improve the quality of our paper.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
Articles in the same Issue
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
