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Unique Continuation and Time Decay for a Higher-Order Water Wave Model.

  • Published In: ESAIM: Control, Optimisation & Calculus of Variations, 2023, v. 29. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Pazoto, Ademir F.; Vieira, Miguel D. Soto 3 of 3

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 [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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:ESAIM: Control, Optimisation & Calculus of Variations. 2023/01, Vol. 29, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2023
  • ISSN:1292-8119
  • DOI:10.1051/cocv/2023040
  • Accession Number:175006741
  • Copyright Statement:Copyright of ESAIM: Control, Optimisation & Calculus of Variations is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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