On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms

@article{Egger2017OnTU,
  title={On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms},
  author={H. Egger and Jan-Frederik Pietschmann and Matthias Schlottbom},
  journal={Inverse Problems},
  year={2017},
  volume={33},
  pages={115005}
}
  • H. Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
  • Published 2017
  • Mathematics
  • Inverse Problems
  • We consider the identification of nonlinear diffusion coefficients of the form $a(t, u)$ or $a(u)$ in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using partial knowledge of the Dirichlet-to-Neumann map. The proof of our main result relies on the construction of a series of appropriate Dirichlet data and test functions with a particular singular behavior at the boundary. This allows us to localize the analysis… CONTINUE READING
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