Control and Stabilization of the Benjamin-Ono Equation in L2(T)

Abstract : We study the control and stabilization of the Benjamin-Ono equation in L2(T), the lowest regularity where the initial value problem is well-posed. This problem was already initiated in Linares and Rosier (Trans Am Math Soc 367:4595–4626, 2015) where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the L2–norm. Moreover, by proving a theorem of controllability in L2, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in Molinet and Pilod (Anal PDE 5:365–395, 2012) and some new extension of these estimates established here.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01261694
Contributeur : François Chaplais <>
Soumis le : lundi 25 janvier 2016 - 17:07:53
Dernière modification le : mardi 14 mai 2019 - 10:32:41

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Camille Laurent, Felipe Linares, Lionel Rosier. Control and Stabilization of the Benjamin-Ono Equation in L2(T). Archive for Rational Mechanics and Analysis, Springer Verlag, 2015, 218 (3), pp.1531-1575. ⟨10.1007/s00205-015-0887-5⟩. ⟨hal-01261694⟩

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