Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
Analysis of PDEs
2024-02-06 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2305.01969,
title = {Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions},
author = {Yacine Chitour and Hoai-Minh Nguyen and Christophe Roman},
journal= {arXiv preprint arXiv:2305.01969},
year = {2024}
}