On the controllability of anomalous diffusions generated by the fractional LaplacianReport as inadecuate




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1 CMLS - Centre de Mathématiques Laurent Schwartz 2 MODAL-X - Modélisation aléatoire de Paris X

Abstract : This paper introduces a -spectral observability condition- for a negative self-adjoint operator which is the key to proving the null-controllability of the semigroup that it generates and to estimating the controllability cost over short times. It applies to the interior controllability of diffusions generated by powers greater than 1-2 of the Dirichlet Laplacian on manifolds, generalizing the heat flow. The critical fractional order 1-2 is optimal for a similar boundary controllability problem in dimension one. This is deduced from a subsidiary result of this paper, which draws consequences on the lack of controllability of some one dimensional output systems from Müntz-Szasz theorem on the closed span of sets of power functions.

keyword : interior controllability spectral observability control cost parabolic equation fractional calculus





Author: Luc Miller -

Source: https://hal.archives-ouvertes.fr/



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