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Finite time extinction by nonlinear damping for Schrodinger equation

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arxiv 1007.0077 v2 pith:5ZEGYKIL submitted 2010-07-01 math.AP

Rémi Carles (I3M) , Clément Gallo (I3M) This is my paper · ORCID
classification math.AP
keywords timedampingequationfiniteinitialnonlinearschrodingerassumption
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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.

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