| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 38 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2024027 | |
| Published online | 03 May 2024 | |
Exponential Decay of Solutions of Damped Wave Equations in One Dimensional Space in the Lp Framework for Various Boundary Conditions
1
Laboratoire des signaux et systèmes, Université Paris Saclay, France
2
Laboratoire Jacques Louis Lions, Sorbonne Université, Paris, France
* Corresponding author: hoai-minh.nguyen@sorbonne-universite.fr
Received:
18
January
2023
Accepted:
19
March
2024
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based on the study of the corresponding hyperbolic systems associated with the Riemann invariants. The key ingredient in the study of these systems is the use of the internal dissipation energy to estimate the difference of solutions with their mean values in an average sense.
Mathematics Subject Classification: 35L02 / 35L05 / 93D20 / 93D23
Key words: Damped wave equations / damped hyperbolic system / exponential decay / Riemann invariants
© The authors. Published by EDP Sciences, SMAI 2024
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