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arXiv · 1007.0077

Finite time extinction by nonlinear damping for Schrodinger equation

Rémi Carles·Clément Gallo
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Abstract

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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Rémi Carles, Clément Gallo. 2010-09-15. Finite time extinction by nonlinear damping for Schrodinger equation. https://arxiv.org/abs/1007.0077

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