Inverse Problem

Inverse Problem :: Ideas and Works

1. Inverse Point Source Problem[1][2][3]

We aim to reconstruct the point source with knowledge of Cauchy data, and study the stability of the reconstruction. There are some results on this topic already, we are aware of the fact that the reconstruction is unique, and the stability arguments has been revealed with Frechet derivative. However, I came up with some thought and gave a expression for the stability. However, the recovery is very nice in simulation.

Books for further reading

1. Elliptic Partial Differential Equations of Second Order, by David Gilbarg, Neil S. Trudinger.
2. The Analysis of Linear Differential Operators Vol.1,2,3,4, by Lars Hormander.
3. An Introduction to the mathematical theory of inverse problems, by Andreas Kirsch.