Sur la théorie de la diffusion pour l'équation de Klein-Gordon dans la métrique de Kerr

Dietrich Häfner

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Index des auteurs, volumes 25-50. Author index, volumes 25-50

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The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic...

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We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension $N \geq 2 .$ Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

Index des tomes LI-LXX (1990-1998)

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Sur les paires d'équations pré-Schröder et leur équivalence

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Pairs of functional pre-Schröder equations (Sₙ) are considered. We show that under some assumptions the system of two equations (S₃), (Sₙ) for some n ≥ 4 is equivalent to the system of all equations (Sₙ) for n ≥ 2. The results answer a question of Gy. Targonski [5] in a particular case.