METIVIER, Guy

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METIVIER, Guy
Institut de Mathématiques de Bordeaux [IMB]

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In this paper we give a class of hyperbolic systems, which includes systems with constant mutliplicities but significantly wider, for which the initial boundary value problem with source term and initial and boundary data in $L^2$, is well posed in $L^2$, provided that the necessary uniform Lopatinski condition is satisfied. Moreover, the speed of propagation is the speed of the interior problem. In the opposite direction, we show on an example that, even for symmetric systems in the sense of Friedrichs, with variable coefficients and variable multiplicities, the uniform Lopatinski condition is not sufficient to ensure the well posedness of the IBVP.< Réduire

Mots clés en anglais

initial boundary value problems

Hyperbolic

systems of partial differential equations

symmerizers

energie estimate

finite speed of propgagation

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On the $L^2$ well posedness of Hyperbolic Initial Boundary Value Problems

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Résumé en anglais

Mots clés en anglais

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