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An Insensitizing Control Problem for the Ginzburg–Landau Equation

Author

Listed:
  • Maurício Cardoso Santos

    (Federal University of Paraíba, UFPB)

  • Thiago Yukio Tanaka

    (Federal Rural University of Pernambuco, UFRPE)

Abstract

In this paper, we prove the existence of insensitizing controls for the nonlinear Ginzburg–Landau equation. Here, we have a partially unknown initial data, and the problem consists in finding controls such that a specific functional is insensitive for small perturbations of the initial data. In general, the problem of finding controls with this property is equivalent to prove a partial null controllability result for an optimality system of cascade type. The novelty here is that we consider functionals depending on the gradient of the state, which leads to a null controllability problem for a system with second-order coupling terms. To manage coupling terms of this order, we need a new Carleman estimate for the solutions of the corresponding adjoint system.

Suggested Citation

  • Maurício Cardoso Santos & Thiago Yukio Tanaka, 2019. "An Insensitizing Control Problem for the Ginzburg–Landau Equation," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 440-470, November.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:2:d:10.1007_s10957-019-01569-w
    DOI: 10.1007/s10957-019-01569-w
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