Well-Posedness and Long-Time Dynamics of a Water-Waves Model With Time-Varying Boundary Delay

A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato’s variable norm technique and the Fixed Point Theorem. More significantly, the energy decay for the linearized problem is demonstrated using the energy method.

Authors

Roberto de A. Capistrano–Filho (ORCID: https://orcid.org/0000-0002-1608-1832)
Oscar A. Sierra Fonseca (ORCID: https://orcid.org/0000-0001-5866-1766)
Boumediène Chentouf (ORCID: https://orcid.org/0000-0001-9365-449X)
George J. Bautista (ORCID: https://orcid.org/0000-0003-2396-8631)

Institutions

Universidade Federal de Pernambuco (BR)
Kuwait University (KW)
Universidad Tecnológica de Los Andes (PE)
Fundação Getulio Vargas (BR)

Publication Details

Journal: Asymptotic Analysis
Published: 2025-06-22
DOI: https://doi.org/10.1177/09217134251344395
Primary Topic: Stability and Controllability of Differential Equations
Type: article
Field-Weighted Citation Impact: 0.00

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article

Well-Posedness and Long-Time Dynamics of a Water-Waves Model With Time-Varying Boundary Delay

Roberto de A. Capistrano–Filho, Oscar A. Sierra Fonseca, Boumediène Chentouf, George J. Bautista

Jun 22, 2025

Asymptotic Analysis

Stability and Controllability of Differential Equations

article

Well-Posedness and Long-Time Dynamics of a Water-Waves Model With Time-Varying Boundary Delay

Roberto de A. Capistrano–Filho, Oscar A. Sierra Fonseca, Boumediène Chentouf, George J. Bautista

June 22, 2025article en

Abstract

A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato’s variable norm technique and the Fixed Point Theorem. More significantly, the energy decay for the linearized problem is demonstrated using the energy method.

Asymptotic Analysis

Universidade Federal de Pernambuco (BR), Kuwait University (KW), Universidad Tecnológica de Los Andes (PE), Fundação Getulio Vargas (BR)

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Stability and Controllability of Differential Equations

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Well-Posedness and Long-Time Dynamics of a Water-Waves Model With Time-Varying Boundary Delay — Roberto de A. Capistrano–Filho, Oscar A. Sierra Fonseca, et al. · Asymptotic Analysis (2025) | TGRS Research Map | TGRS