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, utilizing Kato's variable norm technique and the Fixed-Point Theorem. More significantly, the energy decay for the line...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Bautista, G, R de A Capistrano--Filho, Chentouf, B, O Sierra Fonseca
Format: Article
Language:English
Subjects:
Boussinesq equations
Energy methods
Fixed points (mathematics)
Time dependence
Well posed problems
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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, 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.
ISSN:2331-8422