An Insensitizing Control Problem for the Ginzburg–Landau Equation

Maurício Cardoso Santos () and Thiago Yukio Tanaka ()
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Maurício Cardoso Santos: Federal University of Paraíba, UFPB
Thiago Yukio Tanaka: Federal Rural University of Pernambuco, UFRPE

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 2, No 4, 440-470

Abstract: 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.

Keywords: Ginzburg–Landau equation; Carleman estimates; Insensitizing controls; Null controllability; 93C20; 93B05; 93B07; 93C41; 35K40 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01569-w

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