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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2022

Global well-posedness of the KdV Equation on a star-shaped network and stabilization by saturated controllers

Résumé

In this work, we deal with the global well-posedness and stability of the linear and nonlinear Korteweg-de Vries equations on a finite star-shaped network by acting with saturated controls. We obtain the global well-posedness by using the Kato smoothing property for the linear case and then using some estimates and a fixed point argument we deal with the nonlinear system. Finally, we obtain the exponential stability using two different kinds of saturation by proving an observability inequality via a contradiction argument.
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hal-03831316 , version 1 (26-10-2022)

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Hugo Parada, Emmanuelle Crépeau, Christophe Prieur. Global well-posedness of the KdV Equation on a star-shaped network and stabilization by saturated controllers. SIAM Journal on Control and Optimization, 2022, 60 (4), pp.2268-2296. ⟨10.1137/21m1434581⟩. ⟨hal-03831316⟩
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