Optimal control of Allen-Cahn systems

Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented.

Keywords

Allen-Cahn system, parabolic obstacle problems, linear elasticity, mathematical programs with complementarity constraints, optimality conditions, Trust-Region-Newton method

URI

https://doi.org/10.34657/2932
https://oa.tib.eu/renate/handle/123456789/3035

Citation

Blank, L., Farshbaf-Shaker, M. H., Hecht, C., Michl, J., & Rupprecht, C. (2013). Optimal control of Allen-Cahn systems (Vol. 1906). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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