## Third-party-funded project

**Title: **

Mathematical theory of direct and inverse transient eddy current problems

**Project management at the University of Würzburg:**

- Prof. Dr. Bastian von Harrach
, Professur für Inverse Probleme,Tel: 0931-31-86216,Fax: 0931-31-81491,Mail: bastian.harrach@mathematik.uni-wuerzburg.de

**Participating scientists:**

- Dipl.-Math. Lilian Arnold
, Wissenschaftliche Mitarbeiterin,Tel: 0931-31-86327,Fax: 0931-31-81491,Mail: lilian.arnold@mathematik.uni-wuerzburg.de

**Abstract:**

Transient excitation currents generate electromagnetic fields which in turn induce electric currents in proximal conductors. Mathematically, this can be described by partial differential equations, the eddy-current equations, which are obtained by neglecting the dielectric displacement currents in Maxwells equations. The eddy-current equations are of parabolic-elliptic type: In insulating regions, the field instantaneously adapts to the excitation (elliptic behaviour), while in conducting regions, this adaptation takes some time due to the induced eddy currents (parabolic behaviour). Eddy current effects are used for remotely detecting conducting objects and to non-invasively identify flaws inside a conductor. In mathematical terms this leads to the inverse problem of reconstructing the conductivity coefficient in the eddy current equations from knowledge of the solution(s). Goal of the project is to utilize a unified variational theory for the parabolic-elliptic equations to theoretically study identifiability questions in the inverse problem and derive rigorously justified reconstruction strategies.

**Key words:**

eddy current problems

**Projekt period: **
from 08.2010 to 07.2013

**Funding institution: **

DFG ,Granting date: 17.08.2010