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Pré-Publication, Document De Travail Année : 2023

Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions

Résumé

We establish the exponential decay of the solutions of the damped wave equations in one-dimensional space where the damping coefficient is a nowhere-vanishing function of space. The considered PDE is associated with several dynamic boundary conditions, also referred to as Wentzell/Ventzel boundary conditions in the literature. The analysis is based on the determination of appropriate Lyapunov functions and some further analysis. This result is associated with a regulation problem inspired by a real experiment with a proportional-integral control. Some numerical simulations and additional results on closed wave equations are also provided.
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Dates et versions

hal-04085162 , version 1 (02-05-2023)
hal-04085162 , version 2 (02-02-2024)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

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Yacine Chitour, Hoai-Minh Nguyen, Christophe Roman. Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions. 2023. ⟨hal-04085162v2⟩
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