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Interaction contrôlée dans les équations aux dérivées partielles non linéaires. (Controlled interaction in nonlinear partial differential equations). (French) Zbl 0675.35060
This paper treats the following problem: considering a smooth enough solution (i.e. belonging to \(H^ s\), with s big enough), of a strictly hyperbolic equation, describe the wave front set of u in the future, knowing it in the past. In this paper, it is proved, that, if the \(H^ r\)-wave front set of u is known in the past, then, there is an estimate of the \(H^ r\)-wave front set in the future, for r smaller than \(3s-s_ 0\). An example showing that this theorem is essentially optimal is given.
Reviewer: J.Y.Chemin

MSC:
35L75 Higher-order nonlinear hyperbolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
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