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arXiv · 1610.03829

Stabilization of the Gear-Grimshaw system with weak damping

R. A. Capistrano-Filho
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Abstract

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 $[1,4)$.

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R. A. Capistrano-Filho. 2016-10-12. Stabilization of the Gear-Grimshaw system with weak damping. https://doi.org/10.1007/s10883-017-9363-x

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