Control and stabilization of the periodic fifth order Korteweg-de Vries equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 38.

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H$$(𝕋), 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.

DOI : 10.1051/cocv/2018033
Classification : 35Q53, 93B05, 93D15
Mots-clés : Korteweg-de Vries equation, periodic domain, propagation of regularity, exact controllability, stabilization
Flores, Cynthia 1 ; Smith, Derek L. 1

1 
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     title = {Control and stabilization of the periodic fifth order {Korteweg-de} {Vries} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
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Flores, Cynthia; Smith, Derek L. Control and stabilization of the periodic fifth order Korteweg-de Vries equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 38. doi : 10.1051/cocv/2018033. http://www.numdam.org/articles/10.1051/cocv/2018033/

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