Unique continuation and time decay for a higher-order water wave model
Analysis of PDEs
2022-12-02 v1
Abstract
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 [11], 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.
Cite
@article{arxiv.2212.00155,
title = {Unique continuation and time decay for a higher-order water wave model},
author = {Ademir F. Pazoto and Miguel Soto},
journal= {arXiv preprint arXiv:2212.00155},
year = {2022}
}