Introduction to Part I Constrained Optimization, Identification and Control

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


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.


Optimal Control Problem Boundary Control Posteriori Error Estimator Elliptic Variational Inequality Variational Inequality Constraint 
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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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