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Mathematics  2007 

Space Propagation of Instabilities in Zakharov Equations

DOI: 10.1016/j.physd.2008.03.024

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Abstract:

In this paper we study an initial boundary value problem for Zakharov's equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev spaces. We also show that it is well posed in spaces of analytic functions. Several consequences for the physical consistency of the model are discussed.

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