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Optimal control of the obstacle in semilinear variational inequalities

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Abstract

We consider an optimal control problem where the state satisfies an obstacle type semilinear variational inequality and the control function is the obstacle. The state is chosen to be close to a desired profile while the obstacle is not too large in H 10 (Ω), and H 2-bounded. We prove that an optimal control exists and give necessary optimality conditions, using approximation techniques.

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Authors and Affiliations

  1. Département de Mathématiques, Université d’Orléans, Laboratoire MAPMO, UFR Sciences, BP 6759, 45067, Orléans, France

    Maïtine Bergouniou

  2. Mathematics Department, University of Tennessee, Knoxville, TN, 37996-1300, USA

    Suzanne Lenhart

Authors
  1. Maïtine Bergouniou
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  2. Suzanne Lenhart
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Bergouniou, M., Lenhart, S. Optimal control of the obstacle in semilinear variational inequalities. Positivity 8, 229–242 (2004). https://doi.org/10.1007/s11117-004-5009-9

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  • DOI: https://doi.org/10.1007/s11117-004-5009-9

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