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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.01969 |
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| _version_ | 1866910318108606464 |
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| author | Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe |
| author_facet | Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01969 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe Analysis of PDEs 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. |
| title | Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.01969 |