Identification of a temperature dependent heat conductivity from single boundary measurements

摘要

Considering the identification of a temperature dependent conductivity in a quasi-linear elliptic heat equation from single boundary measurements, we proof uniqueness in dimensions n greater than or equal to 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. [References: 24]