On the stabilization of the Korteweg–de Vries equation - Vilmos Komornik (Boletim da Sociedade Paranaense de Matemática, 2010)
We consider the Korteweg–de Vries equation on a bounded intervalwith 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.