Nonlinear Schrodinger equations with repulsive harmonic potential and applications

dc.creatorCarles, Remi
dc.date2002-10-31
dc.date2003-03-14
dc.date.accessioned2026-07-07T04:52:32Z
dc.date.available2026-07-07T04:52:32Z
dc.descriptionWe study the Cauchy problem for Schrodinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the harmonic potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity.
dc.descriptionFinal version, to appear in SIAM J. Math. Anal
dc.identifierhttps://arxiv.org/abs/math/0210481
dc.identifierhttp://arxiv.org/abs/math/0210481
dc.identifierSIAM J. Math. Anal., 35, #4 (2003), 823-843.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65496
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35Q55; 35B05; 35B40; 35P25
dc.titleNonlinear Schrodinger equations with repulsive harmonic potential and applications
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