EXACT CONTROLLABILITY OF NONLINEAR HEAT EQUATIONS IN SPACES OF ANALYTIC FUNCTIONS

Abstract : It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is indeed reachable. In this paper, we pursue the study of the reachable states of parabolic equations based on a direct approach using control inputs in Gevrey spaces by considering a nonlinear heat equation in dimension one. The nonlinear part is assumed to be an analytic function of the spatial variable x, the unknown y, and its derivative ∂ x y. By investigating carefully a nonlinear Cauchy problem in the spatial variable and the relationship between the jet of space derivatives and the jet of time derivatives, we derive an exact controllability result for small initial and final data that can be extended as analytic functions on some ball of the complex plane. 2010 Mathematics Subject Classification: 35K40, 93B05
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01955484
Contributeur : Lionel Rosier <>
Soumis le : vendredi 14 décembre 2018 - 13:33:58
Dernière modification le : samedi 16 mars 2019 - 01:53:10
Document(s) archivé(s) le : vendredi 15 mars 2019 - 16:25:52

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  • HAL Id : hal-01955484, version 1
  • ARXIV : 1812.06637

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Camille Laurent, Lionel Rosier. EXACT CONTROLLABILITY OF NONLINEAR HEAT EQUATIONS IN SPACES OF ANALYTIC FUNCTIONS. 2018. 〈hal-01955484〉

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