# Detecting Interfaces in a Parabolic-Elliptic Problem from Surface Measurements

@article{Frhauf2007DetectingII, title={Detecting Interfaces in a Parabolic-Elliptic Problem from Surface Measurements}, author={Florian Fr{\"u}hauf and Bastian von Harrach and Otmar Scherzer}, journal={SIAM J. Numer. Anal.}, year={2007}, volume={45}, pages={810-836} }

Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we…

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