The Fourier regularization method for identifying the unknown source for the Helmholtz equation

Xiao-Xiao Li, Ping Fan
2019 International Journal of Mathematical Analysis  
In this paper, we discuss the problem of determining an unknown source which depends only on one variable in two-dimensional Helmholtz equation from one supplementary measurement at an internal point. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the Fourier regularization method. For the regularization solution, the stability estimate between the regularization solution and the exact
more » ... ion and the exact solution is given.
doi:10.12988/ijma.2019.9315 fatcat:tcaymlljjna4jhf3t6dgb6qvmm