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A relaxation approach to vector-valued Allen-Cahn MPEC problems. (English) Zbl 1326.49034

Summary: In this paper, we consider a vector-valued Allen-Cahn MPEC problem. To derive optimality conditions we exploit a regularization-relaxation technique. The optimality system of the regularized-relaxed subproblems are investigated by applying the classical result of Zowe and Kurcyusz. Finally, we show that the stationary points of the regularized-relaxed subproblems converge to weak stationary points of the limit problem.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49J45 Methods involving semicontinuity and convergence; relaxation
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities
35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators
35R35 Free boundary problems for PDEs
34G25 Evolution inclusions
65K10 Numerical optimization and variational techniques
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