Abstract
In this paper, we consider the problem for identifying the unknown source in the Poisson equation in a half unbounded domain. A conditional stability result is given and a quasi-boundary value regularization method is presented to deal with this problem. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. Numerical results are presented to illustrate the accuracy and efficiency of this method.MSC:35R25, 47A52, 35R30.
Highlights
1 Introduction Inverse source problems arise in many branches of science and engineering, e.g. heat conduction, crack identification, electromagnetic theory, geophysical prospecting, and pollutant detection
For the heat source identification, there have been a large number of research results for different forms of heat source [ – ]
In [ ], the authors identified the unknown source dependent only on one variable using the method of fundamental solution
Summary
Inverse source problems arise in many branches of science and engineering, e.g. heat conduction, crack identification, electromagnetic theory, geophysical prospecting, and pollutant detection. To the author’s knowledge, there were few papers for identifying an unknown source in the Poisson equation using the regularization method. In [ ], the author identified the unknown point source using the projective method. In [ ], the authors identified the unknown source dependent only on one variable using the method of fundamental solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
