On the stabilization of the Korteweg–de Vries equation - doi: 10.5269/bspm.v28i2.11215

Abstract

We consider the Korteweg–de Vries equation on a bounded interval
with periodic boundary conditions. We prove that a natural mass conserving global feedback exponentially stabilizes the system in all Sobolev norms and we obtain explicit decay rates. The proofs are based on the family of conservation laws for the Korteweg–de Vries equation.