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Journal Articles Differential and integral equations Year : 1993

On the Cauchy problem for a nonlocal, nonlinear Schrödinger equation occuring in plasma Physics, Differential and Integral Equations

Thierry Colin
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Abstract

In this work, our goal is to study the Cauchy problem for some generalization of the following system. iφt + ∆φ = −div(|∇ψ|2∇ψ), ∆ψ = φ. In particular we shall construct solutions in the energy space associ- ated to this system. We give some sufficient conditions on the initial data which ensure that the solutions are global, but we show that in some cases, finite time blow up occures.
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Dates and versions

hal-00848088 , version 1 (25-07-2013)

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  • HAL Id : hal-00848088 , version 1

Cite

Thierry Colin. On the Cauchy problem for a nonlocal, nonlinear Schrödinger equation occuring in plasma Physics, Differential and Integral Equations. Differential and integral equations, 1993, 6 (6), pp.1431-1450. ⟨hal-00848088⟩
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