Abstract
This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.
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Communicated by A. Bensoussan
This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.
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Chavent, G., Kunisch, K. A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation. Appl Math Optim 27, 231–260 (1993). https://doi.org/10.1007/BF01314817
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DOI: https://doi.org/10.1007/BF01314817