Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

KL2015

Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory

​Y-J. Kim, M-G. Lee, Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory, Quart. Appl. Math. 73 (2015), no.3, 419-433
Y-J. Kim, M-G. Lee
conductivity image reconstruction
2015
We show the well-posedness of the conductivity image reconstruction problem with a single set of interior electrical current data and boundary conductivity data. Isotropic conductivity is considered in two space dimensions. Uniqueness for similar conductivity reconstruction problems has been known for several cases. However, the existence and the stability are obtained in this paper for the first time. The main tool of the proof is the method of characteristics of a related curl equation