Abstract
Consider the heat equation with a nonlinear function α in the boundary condition which depends only on the solution u of the initial-boundary value problem. The unknown function α belongs to a set of admissible functions. For this problem the existence of a second Prechet derivative of the control-state mapping is proved. Based on this result a necessary second order optimality condition is formulated. For the investigated objective sufficient second order condition are closely connected with stability estimates. Using the knowledge about stability estimates, it is shown that already for simple cases the usual sufficient conditions can not be fulfilled.
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Rösch, A. (1998). Second Order Optimality Conditions and Stability Estimates for the Identification of Nonlinear Heat Transfer Laws. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8849-3_18
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DOI: https://doi.org/10.1007/978-3-0348-8849-3_18
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9800-3
Online ISBN: 978-3-0348-8849-3
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