| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 49 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2023040 | |
| Published online | 28 June 2023 | |
Unique Continuation and Time Decay for a Higher-Order Water Wave Model
Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, PO Box 68530, CEP 21945-970 Rio de Janeiro, RJ, Brazil
* Corresponding author: ademir@im.ufrj.br
Received:
20
October
2022
Accepted:
16
May
2023
This work is devoted to prove the exponential decay for the energy of solutions of a higher order Korteweg–de Vries (KdV)–Benjamin–Bona–Mahony (BBM) equation on a periodic domain with a localized damping mechanism. Following the method in [L. Rosier and B.-Y. Zhang, J. Diff. Equ. 254 (2013) 141–178], which combines energy estimates, multipliers and compactness arguments, the problem is reduced to prove the Unique Continuation Property (UCP) for weak solutions of the model. Then, this is done by deriving Carleman estimates for a system of coupled elliptic-hyperbolic equations.
Mathematics Subject Classification: 35Q53 / 35B40
Key words: KdV equations / asymptotic behavior
© The authors. Published by EDP Sciences, SMAI 2023
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