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Introduction to Part I Constrained Optimization, Identification and Control

  • Stefan UlbrichEmail author
  • Andreas Griewank
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)

Abstract

In the article Optimal Control of Allen-Cahn Systems the authors Luise Blank, M. Hassan Farshbaf-Shaker, Claudia Hecht, Josef Michl and Christoph Rupprecht report results of their project regarding a control problem for a multi-component Allen-Cahn equation that incorporates elastic effects. This gives rise to a coupled elliptic-parabolic system. Distributed control of the Allen-Cahn equation and Neumann boundary for the stress tensor on a part of the boundary are considered. Existence results and optimality conditions are given for multi-component systems and smooth potential without distributed control. Concerning obstacle potentials, first-order conditions for the limiting systems of approximating problems are given for the boundary control using a penalization approach and for distributed control by a relaxation technique. Finally, there are some numerical results obtained with Trust-Region-Newton-Steihaug-CG method.

Keywords

Optimal Control Problem Boundary Control Posteriori Error Estimator Elliptic Variational Inequality Variational Inequality Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of MathematicsHumboldt-Universität zu BerlinBerlinGermany

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