Abstract
We shall study the convergence rates of the Tikhonov regularizations for the identification of the diffusivity q(x) in a parabolic–elliptic system. The H1 regularization and a mixed Lp–H1 regularization are considered. For the H1 regularization, we present a simple and easily interpretable source condition, under which the regularized solutions will be shown to converge at the standard rate in terms of the noise level of the data. The convergence is analyzed in three different approaches, which result in the same convergence rate but require quite different conditions on the measurement time and the identifying parameters. For the mixed Lp–H1 regularization, we will achieve some desired convergence rate by using the Bregman distance and some new source condition and nonlinearity condition.
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