Weakly closed nonlinear operators and parameter identification in parabolic equations by tikhonov regularization

Abstract

This paper is devoted to studying convergence rates for the tikhonov regularization of nonlinear ill–posed problems from a geometrical point of view. Also the non–attainable case is considered. In our theory, the weak closedness of the operator defining the equation plays a central role. We prove the weak closedness of this operator for two parameter estimation problems in parabolic equations.

Keywords:

• inverse problems
• parameter estimation
• Tikhonov regularization

Additional information

Notes on contributors

Binder Andreas

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Heinz W. Engl

†

Neubauer Andreas

†

Scherzer Otmar

†

Charles W. Groetsch

†