research article

Control and stabilization of the periodic fifth order Korteweg-de Vries equation

Flores, Cynthia
•
Smith, Derek L.  
September 13, 2019
Esaim-Control Optimisation And Calculus Of Variations

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H-s(& x1d54b;), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regularity property, yields a smoothing effect permitting the application of the contraction principle.