Two approaches for the stabilization of nonlinear KdV equation with boundary time-delay feedback

Abstract : This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional system is well-posed for small initial data. The main results of our study are two theorems stating the exponential stability of the nonlinear time delay system. Two different methods are employed: a Lyapunov functional approach (allowing to have an estimation on the decay rate, but with a restrictive assumption on the length of the spatial domain of the KdV equation) and an observability inequality approach, with a contradiction argument (for any non critical lengths but without estimation on the decay rate). Some numerical simulations are given to illustrate the results.
Type de document :
Pré-publication, Document de travail
Rapport LAAS n° 17433. 2017
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https://hal.laas.fr/hal-01643321
Contributeur : Lucie Baudouin <>
Soumis le : lundi 27 novembre 2017 - 13:50:59
Dernière modification le : vendredi 14 septembre 2018 - 11:55:44

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  • HAL Id : hal-01643321, version 1
  • ARXIV : 1711.09696

Citation

Lucie Baudouin, Emmanuelle Crépeau, Julie Valein. Two approaches for the stabilization of nonlinear KdV equation with boundary time-delay feedback. Rapport LAAS n° 17433. 2017. 〈hal-01643321〉

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