Detecting Interfaces in a Parabolic-Elliptic Problem from Surface Measurements

  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.},
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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