Stabilization of the Gear-Grimshaw system on a periodic domain

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.

arXiv comment18 pages

References in corpus (1)

• Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain

Cited by in corpus (2)

• Pointwise control of the linearized Gear-Grimshaw system
• Stabilization of the Gear-Grimshaw system with weak damping