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arXiv · 1303.4759

Stabilization of the Gear-Grimshaw system on a periodic domain

Roberto A. Capistrano-Filho·Vilmos Komornik·Ademir F. Pazoto
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Abstract

This paper is devoted to the study of a nonlinear coupled system of two Korteweg-de Vries equations in a periodic domain under the effect of an internal damping term. The system was introduced Gear and Grimshaw to model the interactions of two-dimensional, long, internal gravity waves propagation in a stratified fluid. Designing a time-varying feedback law and using a Lyapunov approach we establish the exponential stability of the solutions in Sobolev spaces of any positive integral order.

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Roberto A. Capistrano-Filho, Vilmos Komornik, Ademir F. Pazoto. 2013-03-19. Stabilization of the Gear-Grimshaw system on a periodic domain. https://doi.org/10.1142/s0219199714500473

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