Identification of a Temperature Dependent Heat Conductivity from Single Boundary Measurements

  • Authors:

  • Philipp Kügler

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 2003

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Abstract

Considering the identification of a temperature dependent conductivity in a quasilinear elliptic heat equation from single boundary measurements, we proof uniqueness in dimensions $n \ge 2$. Taking noisy data into account, we apply Tikhonov regularization in order to overcome the instabilities. By using a problem-adapted adjoint, we give convergence rates under substantially weaker and more realistic conditions than required by the general theory. Our theory is supported by numerical tests.