Stabilization of the Gear-Grimshaw system with weak damping

The aim of this work is to consider the internal stabilization of a nonlinear coupled system of two Korteweg--de Vries equations in a finite interval under the effect of a very weak localized damping. The system was introduced by Gear and Grimshaw to model the interactions of two-dimensional, long,...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-02
Main Author: Capistrano-Filho, R A
Format: Article
Language:English
Subjects:
Damping
Gravitational waves
Gravity waves
Stabilization
Two dimensional models
Wave propagation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this work is to consider the internal stabilization of a nonlinear coupled system of two Korteweg--de Vries equations in a finite interval under the effect of a very weak localized damping. The system was introduced by Gear and Grimshaw to model the interactions of two-dimensional, long, internal gravity waves propagation in a stratified fluid. Considering feedback controls laws and using Compactness--Uniqueness Argument, which reduce the problem to use a unique continuation property, we establish the exponential stability of the weak solutions when the exponent in the nonlinear term ranges over the interval \([1,4)\).
ISSN:2331-8422
DOI:10.48550/arxiv.1610.03829