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

Finite time extinction by nonlinear damping for Schrodinger equation