On the periodic Schrödinger-Debye equation

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dc.creatorArbieto, Alexander
dc.creatorMatheus, Carlos
dc.date2005-11-25
dc.date.accessioned2026-07-07T06:51:44Z
dc.date.available2026-07-07T06:51:44Z
dc.descriptionWe study local and global well-posedness of the initial value problem for the Schrödinger-Debye equation in the \emph{periodic case}. More precisely, we prove local well-posedness for the periodic Schrödinger-Debye equation with subcritical nonlinearity in arbitrary dimensions. Moreover, we derive a new \emph{a priori} estimate for the $H^1$ norm of solutions of the periodic Schrödinger-Debye equation. A novel phenomena obtained as a by-product of this \emph{a priori} estimate is the global well-posedness of the periodic Schrödinger-Debye equation in dimensions $1,2$ and 3 \emph{without} any smallness hypothesis of the $H^1$ norm of the initial data in the ``focusing'' case.
dc.identifierhttps://arxiv.org/abs/math/0511634
dc.identifierhttp://arxiv.org/abs/math/0511634
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105087
dc.subjectAnalysis of PDEs
dc.titleOn the periodic Schrödinger-Debye equation
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