Communication Dans Un Congrès Année : 2023

Stability of linear KdV equation in a network with bounded and unbounded lengths

Résumé

In this work, we study the exponential stability of a system of linear Korteweg-de Vries (KdV) equations interconnected through the boundary conditions on a star-shaped network structure. On each branch of the network we define a linear KdV equation defined on a bounded domain (0, ℓj) or the half-line (0, ∞). We start by proving well-posedness using semigroup theory and then some hidden regularity results. Then, we state the exponential stability of the linear KdV equation by acting with a damping term on not all the branches. This is proved by using compactness argument deriving a suitable observability inequality.

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Dates et versions

hal-04170371 , version 1 (25-07-2023)

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Hugo Parada, Emmanuelle Crépeau, Christophe Prieur. Stability of linear KdV equation in a network with bounded and unbounded lengths. CDC 2023 - 62nd IEEE Conference on Decision and Control, Dec 2023, Singapour, Singapore. pp.6199-6204, ⟨10.1109/CDC49753.2023.10383759⟩. ⟨hal-04170371⟩
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