| Issue |
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
|---|---|---|
| Article Number | 93 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2021087 | |
| Published online | 20 September 2021 | |
Stability estimate for the semi-discrete linearized Benjamin-Bona-Mahony equation*,**
1
Departamento de Matemática, Universidad Técnica Federico Santa María,
Valparaiso, Chile.
2
Centro de Modelamiento Matemático, IRL 2807 CNRS-UChile, Universidad de Chile,
Santiago, Chile.
3
Departamento de Ingeniería Matemática, Universidad de Chile,
Santiago, Chile.
*** Corresponding author: jortega@dim.uchile.cl
Received:
26
November
2020
Accepted:
29
August
2021
In this work we study the semi-discrete linearized Benjamin-Bona-Mahony equation (BBM) which is a model for propagation of one-dimensional, unidirectional, small amplitude long waves in non-linear dispersive media. In particular, we derive a stability estimate which yields a unique continuation property. The proof is based on a Carleman estimate for a finite difference approximation of Laplace operator with boundary observation in which the large parameter is connected to the mesh size.
Mathematics Subject Classification: 35B60 / 35L05 / 35Q35 / 35R45 / 65M06
Key words: Benjamin-Bona-Mahony equation / unique continuation property / Carleman estimate discrete Carleman inequalities / dispersive equations / water wave equation / finite difference method / semi-discrete equations
This work is dedicated to Prof. Enrique Zuazua. Dear Enrique, thanks for these years of friendship and for your valuable contributions to the study of control and partial differential equations, and also, for the formation of several generations of researchers in Latin America.
A. Pérez was founded by the National Agency for Research and Development (ANID)/Scholarship Program/ Doctorado Nacional Chile/2017 – 21170495. R. Lecaros was partially supported by FONDECYT(Chile) Grant 11180874. J.H. Ortega was partially supported by Centro de Modelamiento Matemático (AFB170001) and FONDECYT(Chile) Grant 1201125.
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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