A unique continuation result for a system of nonlinear differential equations

Article Sidebar

PDF
Published: May 22, 2023
DOI: https://doi.org/10.5556/j.tkjm.55.2024.5126
Keywords:
Nonlinear equations Long waves Carleman estimate Unique continuation

Main Article Content

Alex M Montes
University of Cauca
Ricardo Córdoba
University of Cauca

Abstract

Using an appropriate Carleman-type estimate, we establish a result of unique continuation for a special class of one-dimensional systems that model the evolution of long water waves with small amplitude in the presence of surface tension.

Article Details

How to Cite
Alex M Montes, & Ricardo Córdoba. (2023). A unique continuation result for a system of nonlinear differential equations. Tamkang Journal of Mathematics. https://doi.org/10.5556/j.tkjm.55.2024.5126
Issue
Online First
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

J. Bona, N. Tzvetkov, Sharp well-posedness results for the BBM equations, Discret. Contin. Dyn. Syst., 23 (2009), 1241-1252.

J. Bourgain, On the compactness of the support of solutions of dispersive equations, Internat. Math. Res. Notices, 5 (1997), 437-447.

M. Davila, G. Perla Menzala, Unique continuation for the Benjamin-Bona-Mahony and Boussinesq's equations, Nonlinear Differ. Equ. Appl., 5 (1998), 367-382.

C. Kenig, G. Ponce, L. Vega, On the support of solutions to the generalized KdV equation, Ann. Inst. H. Poincaré Anal. Non. Lin'earire, 19 (2) (2002), 191-208.

J. Quintero, Solitary water waves for a 2D Boussinesq type system, J. Part. Diff. Eq., 23 (2010), 251-280.

J. Quintero, A. Montes, Existence, physical sense and analyticity of solitons for a 2D Boussinesq-Benney-Luke System, Dynamics of PDE, 10 (2013), 313-342.

J. Quintero, A. Montes, Periodic solutions for a class of one-dimensional Boussinesq systems, Dynamics of PDE., 13 (2016), 241-261.

J. Quintero, A. Montes, On the Cauchy and solitons for a class of 1D Boussinesq systems, Diff. Eq. Dyn. Syst., 24 (2016), 367-389.

J.C. Saut, B. Scheurer, Unique continuation for some evolution equations, J. Diff. Equations, 66 (1987), 118-139.

Y. Shang, Unique continuation for the symmetric regularized long wave equation, Mathematical Methods in Applied Sciences, 30 (2007), 375-388.

B. Zhang, Unique continuation for the Korteweg-de Vries equation, SIAM J. Anal., 23 (1992), 55-71.