Article Dans Une Revue Mathematical Control and Related Fields Année : 2025

Stabilization of Kawahara equation with saturated internal or boundary feedback controls

Résumé

In this paper, we study the stabilizability of the Kawahara equation in a bounded interval (0,L) by a saturated internal control and boundary feedback. We prove the exponential stabilization of the corresponding closed-loop system. We first show the well-posedness of the nonlinear system using linear, nonlinear semigroup theory and fixed-point arguments. Next, we prove two stabilization results by means of interior-saturating feedback and boundary-saturated feedback as well, using observability inequalities and certain unique continuation principle.

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Dates et versions

hal-04314431 , version 1 (29-11-2023)
hal-04314431 , version 2 (26-09-2024)

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Subrata Majumdar, Hugo Parada. Stabilization of Kawahara equation with saturated internal or boundary feedback controls. Mathematical Control and Related Fields, 2025, 15 (3), pp.845-875. ⟨10.3934/mcrf.2024051⟩. ⟨hal-04314431v2⟩
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