Finite time extinction by nonlinear damping for the Schrodinger equation

Rémi Carles (1) , Clément Gallo (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Carles, Clément Gallo. Finite time extinction by nonlinear damping for the Schrodinger equation. Communications in Partial Differential Equations, 2011, 36 (6), pp.961-975. ⟨10.1080/03605302.2010.531074⟩. ⟨hal-00496616v2⟩