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Pré-Publication, Document De Travail Année : 2023

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

Hugo Parada

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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  • HAL Id : hal-04170371 , version 1

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Hugo Parada, Emmanuelle Crépeau, Christophe Prieur. Stability of linear KdV equation in a network with bounded and unbounded lengths. 2023. ⟨hal-04170371⟩
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