Initial boundary value problem and asymptotic stabilization of the Camassa–Holm equation on an interval

Vincent Perrollaz (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We investigate the nonhomogeneous initial boundary value problem for the Camassa-Holm equation on an interval. We provide a local in time existence theorem and a weak strong uniqueness result. Next we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law.

Mots clés: Camassa-Holm equation; initial boundary value problem; PDE control; asymptotic stabilization AMS subject classifications 35Q53; 35G30; 76B15; 93C20; 93D20

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Vincent Perrollaz. Initial boundary value problem and asymptotic stabilization of the Camassa–Holm equation on an interval. Journal of Functional Analysis, 2010, 259, pp.2333 - 2365. ⟨10.1016/j.jfa.2010.06.007⟩. ⟨hal-01108948⟩