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Abstract
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In this talk, the existence of a solution blowing up in finite time will be proved for some Schroedinger equation with complex coefficient in its nonlinearity, even if the initial data is as small as we like. When we consider this kind of problem in whole space, the dispersion of the Schroedinger equation always interrupts the blowing-up estimate of the solution. To overcome this difficulty, we first determine a blowing-up profile and next construct the blowing-up solution by attaching perturbation.
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