WIAS Preprint No. 1858, (2013)

Optimal control of elastic vector-valued Allen--Cahn variational inequalities


  • Farshbaf Shaker, Mohammad Hassan
    ORCID: 0000-0003-0543-5938
  • Hecht, Claudia

2010 Mathematics Subject Classification

  • 35K86 49K20 49K21 49J20 35R35


  • Vector-valued Allen--Cahn system, parabolic obstacle problems, linear elasticity, MPCCs, mathematical programs with complementarity constraints, optimality conditions




In this paper we consider a elastic vector-valued Allen--Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

Appeared in

  • SIAM J. Control Optim., 54 (2016) pp. 129--152.

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