Article ID Journal Published Year Pages File Type
1897993 Physica D: Nonlinear Phenomena 2008 8 Pages PDF
Abstract

This paper is concerned with the standing waves eiωtϕ of Hartree equation with harmonic potential. Via construction of a cross-constrained invariant set for Hartree equation with harmonic potential, it is shown that if the initial data is in the invariant set then the corresponding solution blows up in finite time. Under an appropriate assumption on the frequency ωω, the strong instability of standing waves is investigated by the above blow-up result. Furthermore, without the assumption we also study the property of the standing waves for Hartree equation with harmonic potential.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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